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ADAO79 917 ARMY ENGIMEER WATERNAYS EXPERINENT STATION VICKSBURS MS F/9 8/1ASTATE-OF-THE-ART FOR ASSESSING EARTHQUAKE HAZARDS IN THE UNITED--EC(U)NOV 79 J R HOUSTON
UNCLASSIFIED WES-MP-S-73-1-15 L
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IIIIIIIIIIIIII_
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MISCELLANEOUS PAPER S-73.1I
STATE-OF-THE-ART FOR ASSESSINGEARTHQUAKE HAZARDS IN THE
UNITED STATESk.Reprt 15
- - TSUNAMIS, SEICHES, AND LANDSLIDE-INDUCEDWATER WAVES
- byI. James R. Houston0 Hydraulics LabStatirn
U. S. rn Enginee Waterways EimentStioP. 0.Box 631, Vicksburg, Miss. 39180D D
Pkirmd for Office, Chief of Engineers, U. S. ArmyWashington, D. C 20314~
mnitmwe by Geobechnical LaboratoryU. S. Army Engineer Waterways Experimient Station
P.O0. Box 631, Vicksburg, Miss. 39180LA'7n
10. --. MON
When this report is no longer needed, return it tothe originator.
The findings in this report are not to be construed as an officialDepartment of the Army position unless so designated
by other authorized documents.
Li 1
Unclassified
SECURITY CLASSIFICATION OF THIS PAGE (noen Date shtere
9 Miscellaneous aper-3-
.STATE-OF-THE, ART FOR__SSESSINGARTHQUAKEJAZARDS Report 15 of a series
AN~D ANk LIDE-LDUCED WATER WA6 EFRMN R.REOTNME
aesR. Houston
1I. COUTROLLINO OFFICE NAME AND ADDRESS
Office, Chief of Engineers, U. S. Army NvnIIII17
Washington, D. C. 20314 9014. MONITORING AGENCY NAME & ADDRESSIl different from, Controlling Office) IS. SECURITY CLASS. (of this report)
U. S. Army Engineer Waterways Experiment Station UnclassifiedGeotechnical LaboratoryIS.DLAIIATODONADNP. 0. Box 631, Vicksburg, Miss. 39180 SCHEDULE
1S. DISTRIBUTION STATEMENT (of thie Report)
Approved for public release; ditiu~ 1t
17. DISTRIBUTION STATEMENT (.1 he abstract enitered in Block 20, If diffoenmt from Report)
IS. SUPPLE1116* h N E
19. KEY WORDS (Continue on reverse olde If necessary and Identify by block numtber)
Earthquake damage SeichesEarthquake engineering State-of-the-art-studiesEarthquake hazards TsunamisLandslides Water waves
TRACT (Cfium m reves stab N neevay ong idendify by block numiber)
State-of-the-art methods are presented to assess the hazards of tsunamis,
seiches, and landslide-induced water waves in the United States. Tsunami hazardmaps for the United States are shown that display tsunami elevation zones thathave a 90 percent probability of not being exceeded in a 50-year period.Methods used to determine forces exerted on structures by tsunamis are de-scribed. Hydrodynamic aspects of seiches and landslide-induced water waves are
discussed, as well as methods of assessing the hazards associated with thesephenomena.
DD ji~ CINNtfO OF INOV 65SIS OBSOLETE UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE
(03
UinglassifiedSECURITY CLASSIFICATION OF THIS PACC(ghe, Oats Bmtww*
UnclassifiedSCCURITY CLASSIFICATION OF THIS PAGE~ftenf Data Rnt*,.41
I~A
PREFACE
This report was prepared by Dr. James R. Houston of the Hydraulics
Laboratcry o' the U. S. Army Engineer Waterways Experiment Station (WES),
as part ,f ongoing work at WES in Civil Works Investigation Studies,
"Seismic Effects of Reservoir Loading," sponsored by the Office, Chief
of Engineers, U. S. Army. This is the fifteenth of a series of state-of-
the-art reports for determining the hazards of earthquakes in the United
States.
Preparation of the report was under the direction of Dr. E. L.
Krinitzsky, Engineering Geology and Rock Mechanics Division (EG&RMD),
Geotechnical Laboratory (GL). General direction was by Mr. J. P. Sale,
Chief, GL, and Dr. D. C. Banks, Chief, EG&0M3.
COL Nelson P. Conover, CE, was Commander and Director of WES during
the period of this study. Mr. F. R. Brown was Technical Director.
AQC03..cn r\DC VLB
Jutii ica .------
1 y.- --
1
COTET
j Page
PREFACE . 1
CONVERSION FACTORS, U. S. CUSTOMARY TO METRIC (SI)UNITS OF MEASUREMENT .. ...................... 3
PART I: INTRODUCTION. .. ...................... 4Definitions .. ......................... 4Purpose .. ........................... 4
PART II: TSUNAMIS .. ........................ 6Background. .. ......................... 6Tsunami Hazard in the United States .. ............ 7Tsunami Characteristics. ................... 17
PART III: TSUNAMI MODELING .. ................ ... 22
Hydraulic Scale Models .. ................... 22Analytical Methods .. ..................... 23Numerical Models .. ................... ... 24
PART IV: TSUNAMI ELEVATION PREDICTIONS .. ............. 34
Predictions Based upon Historical Data .. ........... 34Predictions Based upon Historical Data
and Numerical Models .. ................... 36Risk Calculation .. ................ ...... 46Tsunami Hazard Maps. ..................... 46
PART V: THE TSUNAMI WARNIITG SYSTEM .. ............... 57
PART VI: TSUNAMI STRUCTURAL DAMAGE .. ............... 63Introduction.. ............... ... ....... 63Forces .. ................... ........ 64
PART VII: SEICHES. .................. ...... 72
Introduction .................................................72
Modeling of Seiches......................73
PART VIII: LANDSLIDE-INDUCED WATER WAVES .. ............ 75Introduction .. ................ ........ 75Modeling of Landslides .. ................... 77
REFERENCES. ............... ............. 79
APPENDIX A: NOTATION .. ............... ....... Al
2
i/
CONVERSION FACTORS, U. S. CUSTOMARY TO METRIC (SI)UNITS OF MEASUREMENT
U. S. customary units of measurement used in this report can be con-
verted to metric (SI) units as follows:
Multiply By To Obtain
cubic feet 0.02831685 cubic metres
cubic yards 0.7645549 cubic metres
feet O.30148 metres
feet per second 0.3048 metres per second
feet per second squared 0.3048 metres per second squared
miles (U. S. statute) 1.609344 kilometres
miles per hour (U. S. statute) 1.609344 kilometres per hour
pounds (force) 4.448222 newtons
pounds (force) per square foot 47.88026 pascals
pounds (mass) 0.14535924 kilograms
slugs (mass) 14.5939 kilograms
slugs (mass) per cubic foot 515.3788 kilograms per cubic metre
square feet 0.09290304 square metres
tons (2000 lb, mass) 907.1847 kilograms
yards 0.9144 metres
3
STATE-OF-THE-ART FOR ASSESSING EARTHQUAJM
HAZARDS IN THE UNITED STATES
TSUNAMIS, SEICHES, AND LANDSLIDE-INDUCED
WATER WAVES
PART I: INTRODUCTION
Definitions
1. Tsunamis, seiches, and landslide-induced water waves are
secondary phenomena associated with earthquakes. Tsunamis are long-
period sea waves usually generated by earthquakes that cause a deforma-
tion of the sea bed. Coastal and submarine landslides and volcanic
eruptions also have triggered tsunamis. The term "tsunami" originates
from the Japanese words "tsu" (harbor) and "nami" (wave). This associa-
tion with waves in a harbor probably is related to the large tsunami
elevations that sometimes occur in harbors as a result of resonant ampli-
fication of tsunamis by partially enclosed bodies of water. Seiches are
oscillations of enclosed bodies of water that may be induced by earth-
quakes. Oscillations produced in a harbor by a tsunami are sometimes
referred to as seiches; however, a seiche is properly an oscillation of
an enclosed body of water such as a lake or reservoir. Seiches are quite
often produced by atmospheric phenomena rather than seismic events.
Seismic events also can trigger landslides that fall into bodies of water
and produce waves. These landslides may occur in coastal areas (result-
ing waves usually referred to as a tsunami) or enclosed bodies of water
such as lakes or reservoirs.
Purpose
2. The purpose of this report is to present the state of the
art for assessing the hazards of tsunamis, seiches, and landslide-
induced water waves in the United States. The report is primarily
L1
/
concerned with hydrodynamic aspects in assessing hazards. For example,
methods to determine the hydrodynamic consequences of a landslide (given
that the landslide occurred) are presented and not methods to determine
the possibility that the landslide would occur.
I5
/1
PART II: TSUNAMIS
Background
3. Although tsunamis are secondary phenomena, they can produce
great destruction and loss of life. For example, the Great Hoei Tokaido-
Nanhaido tsunami of Japan killed 30,000 people in 1707. In 1868, the
Great Peru tsunami caused 25,000 deaths. The Great Meiji Sanriku tsunami
of 1896 killed 27,122 persons in Japan and washed away over 10,000
houses (Iida et al., 1967).
4. Tsunamis have taken many lives in the United States, with more
people having died since the end of World War II as a result of tsunamis
than as a result of the direct effects of earthquakes. For example,
the Great Aleutian tsunami of 1946 killed 173 people in Hawaii and pro-
duced $26 million in property damage in the city of Hilo, Hawaii. The
1960 Chilean tsunami killed 61 people in Hawaii and caused $23 million
in property damage (Pararas-Carayannis, 1978). The most recent
major tsunami to affect the United States, the 1964 Alaskan tsunami,
killed 107 people in Alaska, 4 in Oregon, and 11 in Crescent City,
California, and caused over $100 million in damage on the west coast of
North America (Wilson and Torum, 1968).
5. A major difference in the destructive characteristics of earth-
quakes and tsunamis is that earthquakes are locally destructive, whereas
tsunamis are destructive locally as well as at locations distant from the
area of tsunami generation. For example, the 1960 Chilean earthquake
caused destruction in Chile but went unnoticed in the United States ex-
cept for the recordings of seismographs. However, the tsunami generated
off the coast of Chile by this earthquake not only killed over 300 people
in Chile and caused widespread devastation, but also killed 61 people in
Hawaii and produced widespread destruction in distant Japan where 199
people were killed, 5000 structures wrecked or washed away, and over
7500 boats wrecked or lost (lida et al., 1967).
6. Tsunamis are principally generated by undersea earthquakes of
magnitudes greater than 6.5 on the Richter scale. The typical height of
6
a tsunami in the deep ocean is less than a foot, and the wave period is
5 min to several hours. Tsunamis travel at hallow-water wave
celerity equal to the square root of the a in due to gravity
times the water depth even in the deepest c 2ause of their very
long wavelengths. This speed of propagation can be in excess of 500 mph*
in the deep ocean.
7. When tsunamis approach a coastal region where the water depth
decreases rapidly, wave refraction, shoaling, and bay or harbor resonance
may result in significantly increased wave heights. The great period
and wavelength of tsunami waves preclude their dissipating energy as a
breaking surf; instead, they are apt to appear as rapidly rising water
levels and only occasionally as bores.
Tsunami Hazard in the United States
Atlantic and Gulf Coasts
8. The seismic activity of the Atlantic Ocean region is relatively
low. In general, coasts bordering the Atlantic Ocean are not paralleled
by lines of tectonic, seismic, or volcanic activity. They are rarely
associated with structural discontinuities like those along the circum-
Pacific seismic belt where fully 80 percent of the world's earthquakes
occur. Only about 10 percent of all reported tsunamis have been in the
Atlantic Ocean region.
9. The possibility of significant elevations on the Atlantic or
the Gulf Coast of the United States produced by distantly generated
tsunamis is very small. With the exception of the Portugal-Morocco
region, the eastern Atlantic has a very low level of seismic activity.
For example, the largest known shock for a thousand years in the area of
Great Britain occurred in the North Sea in 1931 and had a magnitude of
only 5-1/2 (Gutenberg and Richter, 1965). The Atlantic Coast of France
and all of the eastern coast of Africa south of Morocco have a similar
A table of factors for converting U. S. customary units of measure-ment to metric (SI) units is presented on page 3.
7_
low level of seismic activity. Large earthquakes do occur in certain
areas of the midoceanic ridges. However, earthquakes that occur on
crests of the mid-Atlantic ridge not associated with know, fracture zones
show either normal faulting, the tension axis being horizontal and
perpendicular to the local strike of the ridge, or strike-slip motion of
transform faulting. Earthquakes on the fracture zones of the mid-
Atlantic ridge also are characterized by a predominance of strike-slip
motion (Sykes, 1972). Large tsunamis, however, are generated by vertical
ground motion (Wiegel, 196h), and only small amounts of vertical motion
may accompany strike-slip motion or normal faulting with a horizontal
tension axis. Consequently, although there have been many local tsunamis
in the Azores Islands of the mid-Atlantic ridge, no earthquake there or
anywhere along the mid-Atlantic ridge has ever produced a tsunami re-
ported on any Atlantic coastline.
10. Large earthquakes have occurred in the Portugal-Morocco region
(1356, 1531, 1597, 1722, 1755, 1761, 1773, 1926, 1960). The largest
known Atlantic earthquake, and indeed one of the largest known earth-
quakes of historic times, occurred off the coast of Portugal on 1 Novem-
ber 1755. This earthquake generated the most destructive tsunami ever
reported in the Atlantic. Tsunamis generated by this earthquake were
reported in the West Indies. The sea rose 12 ft several times at Antigua,
and every 5 min afterwards for 3 hr it rose 5 ft. The sea retired so
far at St. Martin Island that a sloop riding at anchor in 15 ft of water
was laid dry on her broadside. On the island of Saba, the sea rose 21 ft.
At Martinique and most of the French Islands, the sea overflowed the
lowland, returning quickly to its former limits (Davidson, 1936). Reid
(1914), however, reported that there is little evidence that tsunamis
generated by the 1755 earthquake were noticed on the coasts of the
United States. The orientation of the fault along which this earthquake
occurred is such that waves generated by a seismic event would be
directed toward the West Indies and not the United States. Furthermore,
the great continental shelf off the Atlantic and Gulf Coasts of the
United States is likely to dissipate much of the energy of a tsunami.
Part of the eastern coastline of Florida has a short continental shelf
8
/
and is relatively close to the West Indies. However, the shelf off the
Bahamas Islands probably shelters this area.
11. In the western Atlantic, the main tsunamigenic region is the
subduction zone along the arc of the West Indies Islands. The many
intense earthquakes of this area have had relatively short fault lengths
and, therefore, small source areas for tsunami generation. There have
been no reports of tsunamis generated in this area reaching any distant
coast. The only tsunami known to have been recorded on the Atlantic
Coast of the United States was generated by an earthquake off the
Burin Peninsula of Newfoundland on 18 November 1929. A tsunami from
this Grand Banks earthquake moved up several inlets and obtained a maxi-
mum height of 50 ft. Several villages were destroyed. Tide gages on
the coast of New Jersey recorded the tsunami with a 1-ft elevation at
Atlantic City, New Jersey.
12. The possibility of significant locally generated tsunamis on
the Atlantic or the Gulf Coast of the United States is very remote.
These coastlines do not have structural discontinuities associated with
seismic activity. Crustal structures have been followed by geophysical
and geological methods and appear to dip far under the ocean bottom
without any break (Gutenberg, 1951). Only one large earthquake has
occurred on this coast in historic times. The Charleston, South
Carolina, earthquake of 1886 was one of the largest earthquakes in the
United States, and even one of the greatest occurring anywhere in the
world. There has been no known earthquake in the Atlantic coastal plain
of the United States of even remotely the same magnitude before or
since (Heck, 1947). Despite the large size of the Charleston earth-
quake, no tsunami was generated. McKinley (1887) reported that "Except
in the rivers the wave motion was not observed to have communicated to
the water." Thus, this earthquake probably exhibited little of the
vertical motion required to generate a significant tsunami. The com-
plete lack of tsunamigenic activity on the eastern coast of the United
States is probably a result of not only a low level of seismic activity
but also the strike-slip nature of earthquakes in the area.
13. The tsunami threat from both locally and distantly generated
9
tsunamis is very small on the Atlantic and Gulf Coasts of the United
States and, undoubtedly, less than the threat from hurricane or storm
surges. However, this threat cannot necessarily be neglected when
hazards are investigated for critical facilities such as nuclear power
plants. For such a case, the effects must be considered of a tsunami
such as that generated in Portugal in 1755, or the possibility must be
investigated of the occurrence of a locally generated tsunami such as
the 1929 tsunami generated off the Burin Peninsula of Newfoundland.
Puerto Rico and the Virgin Islands
14. Puerto Rico and the Virgin Islands lie along the subduction
zone of the Lesser Antilles that forms the eastern boundary of the
Caribbean tectonic plate. Earthquakes along this subduction zone
generate important local tsunamis. Tsunamis were generated near the
Virgin Islands in 1867 and 1868 (Heck, 1947). The 1867 tsunami swept
the harbors of St. Thomas and St. Croix. A wall of water 20 ft high
entered these harbors and broke over the lower parts of the towns. At
St. Thomas, the water moved inland a distance of 250 ft. The tsunami
also was large on adjacent islands and the eastern coast of Puerto Rico.
The Alcalde of Yabucoa (southeastern Puerto Rico) reported that the sea
retreated about 150 yd, then returned, and advanced an equal distance
inland. The wave was noted as far as Fajardo (which is 20 miles to the
northeast from the Alcalde of Yabucoa) and as far as h0 to 60 miles
along the southern shore from the Alcalde of Yabucoa (Reid and Taber,
1919).
15. An earthquake and resulting tsunami in November 1918 killed
116 people in Puerto Rico and produced damage reported in excess of
$4 million. During the tsunami, the ocean first withdrew exposing
reefs and stretches of sea bottom not visible during the lowest tides.
The water then returned reaching heights that were greatest near the
northwest corner of Puerto Rico. At Point Borinquen, the tsunami
reached an elevation of 15 ft. Near Point Agujereada, several hundred
palm trees were uprooted by waves from 18 to 20 ft high. At Aguadilla,
waves with heights from 8 to 11 ft were reported. The Columbus Monu-
ment, about 2-1/2 miles southwest of Aguadilla, was thrown down by waves
10
at least 13 ft in height, and rectangular blocks of limestone weighing
over a ton were washed inland distances as great as 250 ft. Heights of4 ft were reported at Mayaguez, and heights of 3 ft at El Boqueron. The
tsunami was noticeable at Ponce, Isabela, and Arecibo, but not at San
Juan. Elevations of 13 ft were reported on the west coast of Mona
Island (Reid and Taber, 1919).
16. The hazard in Puerto Rico and the Virgin Islands from dis-
tantly generated tsunamis is likely to be less than the hazard from
locally generated tsunamis or hurricane surges. Houston et al. (1975)
demonstrated that a very large earthquake in the Portugal area similar
to that of the 1755 earthquake will not produce an elevation in Puerto
Rico greater than the expected elevations of locally generated tsunamis
or hurricane surges.
Hawaiian Islands
17. As a result of their central location in the Pacific Ocean
(where approximately 90 percent of all recorded tsunamis have occurred),
the Hawaiian Islands have a history of destructive tsunamis. The
earliest recorded tsunami in the Hawaiian Islands was the 1819 tsunami
that was generated in Chile. Over 100 tsunamis have been recorded in
the Hawaiian Islands, and 16 of these tsunamis have produced significant
damage. Pararas-Carayannis (1978) compiled a detailed catalog of
historical observations of tsunamis in the Hawaiian Islands.
18. The distantly generated tsunamis that have produced destruction
in the Hawaiian Islands have originated from the Aleutian Islands, Chile,
the Kamchatka Peninsula of the Soviet Union, and Japan. More than half
of all recorded tsunamis in the Hawaiian Islands were generated in the
Kuril-Kamchatka-Aleutian regions of the northern and northwestern
Pacific, and one fourth were generated along the western coast of South
America. Tsunamis generated in the Philippines, Indonesia, the
New Hebrides, and the Tonga-Kermadec island arcs have been recorded in
the Hawaiian Islands, but they have not been damaging.
19. Locally generated tsunamis also have produced destruction in
the Hawaiian Islands. The 1868 tsunami that was generated on the south-
eastern coast of the big island of Hawaii produced severe destruction
1l
)
on this coast. Runup elevations perhaps as great as 60 ft were reported
during this tsunami. A tsunami generated on 29 November 1975 along the
same southeastern coast of the island of Hawaii produced runup elevationsas great as 45 ft. Loomis (1976) presented a detailed description of
the 1975 tsunami. Cox and Morgan (1977) compiled a detailed description
of locally generated tsunamis in the Hawaiian Islands.
20. The tsunami hazard in the Hawaiian Islands is not uniform.
For example, elevations are generally greater on the northern side of
these islands as a result of the many tsunamis generated in the Kuril-
Aleutian region. Runup elevations on a single island during a tsunami
also may be large at one location and small at another, even at loca-
tions that are separated by short distances. Sometimes the reasons for
these variations are known. For example, the extensive reefs in Kaneohe
Bay on the island of Oahu protect the bay from tsunamis by strongly re-
flecting or dissipating them. Often the reasons for these variations
are not apparent as a result of the complex interactions that occur.
Houston et al. (1977) made elevation predictions based upon historical
data and numerical model calculations for the Hawaiian Islands. These
predictions are discussed in Part IV.
Alaska
21. The Pacific and Americas tectonic plates collide along the
subduction zone of the Aleutian-Alaskan Trench. Boundaries between
tectonic plates are highly seismic with almost 99 percent of all earth-
quakes occurring along these boundaries (Lomnitz, 1973). The great
seismicity of the region and vertical motions associated with the sub-
duction zone make the Aleutian-Alaskan region highly tsunamigenic. The
earliest recorded tsunami in this region occurred in 1788. Four major
tsunamis have been generated since 1946. The 1946 tsunami was generated
in the eastern Aleutian Islands, the 1957 tsunami in the central Aleutian
Islands, the 1964 tsunami in the Gulf of Alaska, and the 1965 tsunami in
the western Aleutian Islands.
22. Figure 1 shows a map of Alaskan localities that have experi-
enced tsunamis. These locations are concentrated along the boundary of
the Pacific and Americas plates. The remainder of Alaska has not had a
12
U o\
"Iar
I-0
-P 4
r+40HL~
:EO
N 44
'AN
13
* reported tsunami. However, this region has a very low population density,
and reporting may be quite poor. Cox and Pararas-Carayannis (1976) pub-
lished a catalog of reported tsunamis in Alaska. Locally generated
tsunamis dominate the catalog.
23. The 1964 Alaskan tsunami demonstrated the tremendous destruc-
tive power of major locally generated tsunamis in Alaska. This tsunami
produced over $80 million in damage and killed 107 people (Wilson and
Torum, 1968). In addition to the waves generated by the large-scale
tectonic displacement, large waves were generated in many areas by
submarine slides of thick sediments.
West coast of thecontinental United States
24. The hazard on the west coast of the United States due to dis-
tantly generated tsunamis has been demonstrated by tsunami activity
since the end of World War II. For example, the 1946 Aleutian tsunami
produced elevations (combined tsunami and astronomical tide) as great as
15 ft above mean lower low water (mllw) at Half Moon Bay, California;
13.4 ft above mllw at Muir Beach, California; 14 ft above mllw at Arena
Cove, California; and 12.4 ft above mllw at Santa Cruz, California. One
person in Santa Cruz was killed by this tsunami. The 1960 Chilean
tsunami produced a trough to crest height of 12 ft at Crescent City,
California, and caused $30,000 in damage to the dock area and streets
(Magoon, 1965). The 1964 Alaskan tsunami produced elevations above mean
high water (mhw) as great as 14.9 ft at Wreck Creek, 9.7 ft at Ocean
Shores, and 12.5 ft at Seaview in the state of Washington. Elevations
from 10 to 15 ft above mhw were produced along much of the coast of
Oregon, and four people were killed. This tsunami reached an elevation
of 20.7 ft above mllw at Crescent City, California. Crescent City
sustained widespread destruction with $7.5 million in damage and 11
deaths (Wilson and Torum, 1968).
25. Tsunamis generated in South America and the Aleutian-Alaskan
region pose the greatest hazard (from distantly generated tsunamis) to
the west coast of the United States. Historical records of tsunami
occurrence in the Hawaiian Islands indicate that tsunamis generated in
14
the Philippines, Indonesia, the New Hebrides, and the Tonga-Kermadec
island arcs do not generate tsunamis that are significant at transoceanic
distances. Tsunamis, such as the 1896 Great Meiji Sanriku and the 1933
Great Shorva Sanriku that were generated off the coast of Japan, have
produced no significant elevations on the west coast of the United States.
Kamchatkan tsunamis, such as the ones in 1923 and 1952 (which were the
greatest from Kamchatka since at least 1837), did not cause damage on
the west coast. The west coast of Canada lies along a strike-slip fault
that has not historically produced tsunamis on the west coast of the
United States. Tsunamis off the Pacific Coast of Mexico have produced
large local elevations, but they are generated by earthquakes covering
areas that are apparently too small to cause significant elevations on
the west coast of the United States.
26. The west coast of the United States lies along the boundary
of the Pacific and Americas tectonic plates. However, this boundary
is not a subduction zone. The Pacific and Americas plates have a hori-
zontal relative motion along this boundary, and earthquakes in the region
exhibit strike-slip motion that is not an efficient generator of tsunamis.
For example, the 1906 Great San Francisco earthquake (8.3 magnitude
on Richter scale) produced waves with heights no greater than 5 cm
(lida et al., 1967).
27. The hazard of locally generated tsunamis on the west coast
of the United States is probably much less than the hazard from distantly
generated tsunamis. However, there have been reports of significant
locally generated tsunamis on the west coast. For example, a recent
publication of the California Division of Mines and Geology (Weber and
Kiessling, 1978) mentions that Wood and Heck (1966) reported that runup
heights of a tsunami generated by the 1812 Santa Barbara earthquake
reached 50 ft at Gaviota, 30-35 ft at Santa Barbara, and 15 ft or more
at Ventura in California. However, an exhaustive study (Marine Advisors,
Inc., 1965) of this event that included an investigation of the unpub-
lished notes (cited by Wood and Heck) of the late Professor G. D.
Louderback, University of California, Berkeley, has shown that the runup
heights for this tsunami probably were not more than 10-12 ft at Gaviota
15
and correspondingly lower at the other locations. A report of a tsunami
at Santa Crux, California, in 1840 also has been shown to be erroneous
(Symons and Zetler, 1960). The largest authenticated locally generated
tsunami on the west coast was generated by the 1927 Point Arguello
earthquake and produced runup elevations as great as 6 tt in the imme-
diate vicinity. Although there is no solid evidence that locally gene-
rated tsunamis pose a great hazard on the west coast, the possibility of
significant locally generated tsunamis cannot be neglected when consid-
ering hazards to critical facilities such as nuclear power plants.
There also is the possibility that locally generated tsunamis may pro-
duce greater runup elevations than are produced by distantly generated
tsunamis in areas protected from distantly generated tsunamis (Puget
Sound, Washington, and parts of southern California).
Pacific Ocean islandterritories and possessions
28. Many of the island territories and possessions of the United
States are parts of seamounts that rise abruptly from the ocean floor.
As a result of the very short transition distance (relative to typical
tsunami wavelengths in the deep ocean) from oceanic depths to the shore-
line of these islands, distantly generated tsunamis do not produce
large elevations on these islands. The maximum elevation produced on
such islands by distant tsunamis is on the order of 1 m (elevation re-
corded at Johnston Island during the 1960 Chilean tsunami by Symons and
Zetler, 1960). Islands in this category include Wake Island, the
Marshall Islands, Johnston Island, the Caroline Islands, the Mariana
Islands, Howland Island, Baker Island, and Palmyra Island. The possi-
bility of elevations on these islands greater than 1 m being produced by
distantly generated tsunamis cannot be neglected if the hazard to
critical facilities is being considered. Detailed investigations of
the response of different islands to tsunamis have not been performed.
It is known that 20-ft elevations were recorded on Easter Island as a re-
sult of the 1960 Chilean tsunami (generated approximately 2000 miles
away). This island is small and the surrounding seamount is fairly
small. The exact transition between seamounts too small to amplify
16
.........
I
tsunamis and those large enough to cause significant amplification is
not known. Numerical models discussed in Part III can be used to deter-
mine the interaction of tsunamis with islands.
29. The Samoa Islands are subject to tsunami flooding. The 1960
Chilean tsunami had a trough to crest height of 15 to 16 ft at the head
of Pago Pago harbor (crest elevation of 9.5 ft) in American Samoa (Keys,
1963). Property damage of $50,000 occurred in Pago Pago village during
this tsuixami. Local tsunamis also are destructive in the Samoa Islands.
A destructive earthquake and 40-ft tsunami have been reported to have
occurred in 1917 (Heck, 1947). Whether this elevation occurred on
American Samoa or one of the other Samoan Islands is not known. However,
the tsunami was destructive at Pago Pago, American Samoa.
Tsunami Characteristics
Generation and
deep-ocean propagation
30. Most tsunamis are generated along the subduction zones border-
ing the Pacific Ocean. These zones are highly seismic and earthquakes
occurring within these jubduction zones often exhibit the vertical dip-
slip motion that is required to produce significant tsunami elevations.
Berg et al. (1970) demonstrated that horizontal or strike-slip motion
is a very inefficient mechanism for the generation of tsunamis.
31. Large tsunamis are associated with elliptically shaped gener-
ating areas that radiate energy preferentially in a direction perpendicu-
lar to the major axis. The major axis of the tsunami is approximately
parallel to the oceanic trench or island arc that is the boundary be-
tween colliding tectonic plates. Momoi (1962) developed a relationship
between the tsunami wave height H in the direction of the major axisa
of a source of length a and the wave height H. in the direction of
the minor axis of length b for an instantaneously and uniformly ele-
vated elliptic source. This relationship is expressed by the equation
Hb/Ha = a/b . Takahasi and Hatori (1962) demonstrated that this equa-
tion was valid by performing laboratory tests using an elliptically
shaped membrane. Hatori (1963) showed that data from historical tsunamis
17
indicated that this equation was reasonable.
32. The directional radiation of energy from the region of genera-
tion of a tsunami is quite important. The ratio of the length of the
major axis to the minor axis for large earthquakes, such as the 1964
Alaskan or the 1960 Chilean earthquake, can be approximately 4 to 6;
thus the waves radiated in the direction of the minor axis can be greater
than those radiated in the direction of the major axis by a similar ratio.
Therefore, the orientation of a tsunami source region relative to a
distant area of interest is very important, and the runup at a distant
site due to the generation of a tsunami at one location along a trench
cannot be considered as being representative of all possible placements
of the tsunami source along the trench region. For example, the 1957
Aleutian tsunami produced significant elevations in the Hawaiian Islands
but was fairly small on most of the west coast of the continental
United States, whereas the 1964 Alaskan tsunami was fairly small in the
Hawaiian Islands and fairly large on the northern half of the west coast.
An earthquake generating a tsunami in an area southwest of the 1964
Alaskan tsunami will beam energy toward the southern half of the west
coast of the United States.
33. The ground motion generating a large tsunami occurs over such
a short time relative to the period of the tsunami that the motion can
be considered to be instantaneous. Typical rise times (time from initia-
tion of ground motion to attainment of permanent vertical displacement)
are in tens of seconds for earthquakes, whereas tsunami periods are in
tens of minutes. Higher frequency oscillations superimposed upon the
movement to a permanent displacement have periods in seconds. The time
for the ground rupture to move the entire length of the source is a few
minutes. Hammack (1972) shows that for a large tsunami, such as the
1964 Alaskan tsunami, the actual time-displacement history of the ground
motion is not important in determining far-field characteristics of the
resulting tsunami. All time-displacement histories reaching the same
permanent vertical ground displacement will produce the same tsunami in
the far field. Hammack also showed that small-scale features of the
permanent ground deformation produce waves that are not significant far
18
from the source region. Thus, distantly generated tsunamis can be
studied knowing only major features of the permanent ground displacement.
34. Tsunamis are generated along continental margins or island
arcs and then propagate out into the deep ocean. The depth transitionfrom the relatively shallow region of generation to the deep ocean occurs
over a very short distance relative to typical tsunami wavelengths in
the deep ocean that are in hundreds of kilometres. In the deep ocean,
tsunami wave heights are a few feet at most. The wave steepness (ratio
of wave height to wavelength) is so small for tsunamis that they go
unnoticed by ships in the deep ocean. Hammack and Segur (1978) demon-
strated that as a result of the small amplitudes and long wavelengths of
large tsunamis of consequence to distant areas, the propagation over
transoceanic distances of the leading wave (or waves, since leading
waves reflected off land areas may arrive at a distant location after
the primary leading wave) in the generating region and in the deep
ocean is governed by the linear long-wave equations. Hammack and Segur
also showed that eventually nonlinear and dispersive effects will become
important in the propagation of a tsunami in the deep ocean, but that
the propagation distance necessary for these effects to become signifi-
cant for the leading wave of a large tsunami (such as the 1964 Alaskan
tsunami) is large compared with the extent of the Pacific Ocean. The
later smaller waves of a tsunami wave train are shown to be ipso facto
frequency dispersive (Hammack and Segur, 1978).
Nearshore effects
35. When tsunamis approach a coastal region where the water- depth
decreases rapidly, wave refraction, shoaling, bay or harbor resontnce,
and other effects may result in significantly increased wave heights.
The dramatic increase in heights of tsunamis often occurs over fairly
short distances. For example, during the 1960 tsunami at Hilo, Hawaii,
waves could be seen breaking over the waterfront area of Hilo from a
ship approximately 1 mile offshore, yet the personnel on the ship
could not notice any disturbance passing by the ship. Tsunamis also
can be quite large at one location and small at nearby locations (e.g.,
19
J _--... ... . ~
they may be large within a harbor as a result of resonant effects and
small on the open coast).
36. As tsunamis enter shallower water, their heights increase and
their wavelengths decrease; therefore, nonlinear and frequency dispersion
effects become more significant. However, Hammack and Segur (1978) and
Goring (1978) showed that the linear long-wave equations are adequate
to describe the propagation of a large tsunami, such as the 196h Alaskan
tsunami, from the deep ocean up onto the continental shelf.
37. Tsunamis usually appear at the shoreline in the form of rapidly
rising water levels but occasionally in the form of bores. When they
appear as bores, frequency dispersion effects are important in the
region of the face of the bore and long-wave equations are not adequate
to describe flow in this region. However, beyond the face of the bore
the water surface has been described as being almost flat in appearance
(McDonald et al., 1947). Long-wave equations may adequately describe
flows in this broad-crested region that probably governs the ultimate
land inundation.
38. Even when a tsunami appears as a rapidly rising water level,
there are many small-scale effects that develop that are highly non-
linear and frequently dispersive (e.g., small bores forming at the
tsunami front during propagation over flatland and strong turbulence
during flow past obstacles and areas of great roughness). However,
there is substantial evidence that the main features of the extent of
land inundation are governed by simple processes. Quite often the runup
elevation (elevation of maximum inundation) is the same as the elevation
near the shoreline and at other locations within the zone of inundation.
Therefore, the water surface of the tsunami is fairly flat during
flooding. For example, Magoon (1965) reported flooding to about the 20-ft
contour above mllw and elevations at the shoreline of about 20 ft for
the 1964 Alaskan tsunami at Crescent City, California. Wilson and Torum
(1968) reported that the 20-ft (mllw) runup at Valdez, Alaska, for the
1964 tsunami checked "well for consistency with water-level measurements
made on numerous buildings throughout the town." Similar comments were
made by Brown (196h) in reference to survey measurements of 30-ft (mllw)
20
runup at Seward, Alaska, for the 1964 Alaskan tsunami. Runup elevations
and elevations at the shoreline and in the inundation zone were similar
at nine locations in Japan as recorded by Nasu (1934) in surveys follow-
ing the 1933 Sanriku tsunami. This tsunami had a short period (12 min)
and reached an elevation as great as 28.7 metres at one survey location.
The runup elevation and the elevation near the shoreline also were
similar at Hilo, Hawaii, for the 1960 tsunami (borelike waves) (Eaton et
al., 1964). Differences are apparent, however, at locations where
Eaton et al. demonstrated that flow divergence is significant. Flow
divergence and convergence, frictional effects, and time-dependent
effects (that can limit the time available for complete flooding) are
probably the major effects causing differences between runup elevations
and elevations near shoreline.
21
PART III: TSUNAMI MODELING
39. The scarcity of historical data of tsunami activity often
makes it necessary to use hydraulic scale models, analytical methods,
or numerical methods to model tsunamis in order to determine quantita-
tively the tsunami hazard. Even at locations with ample historical
data, changes in land elevations and vegetation (thus changes in land
roughness) as a result of development and the building of protective
structures may modify the tsunami hazard. Scale models, analytical
methods, or numerical methods are required to determine the magnitude
of this modification.
Hydraulic Scale Models
40. Although it would not be practical to use hydraulic scale
models (with reasonable scales) to model tsunami propagation across
transoceanic distances, these models have found some applicaton in
simulating tsunami propagation in nearshore regions and interaction with
land areas. For example, hydraulic models have been used to study
tsunami interaction with single islands that are realistically shaped
and surrounded by variable bathymetry. Van Dorn (1970) studied tsunami
interaction with Wake Island using a 1:57,000 undistorted scale model.
Jordaan and Adams (1968) studied tsunami interaction with the island
of Oahu in the Hawaiian Islands using a 1:20,000 undistorted scale
model. They found poor agreement between historical measurements of
tsunami runup and the hydraulic model data. Scale effects (e.g. viscous
effects) and the effects of the arbitrary boundariet that confine the
hydraulic model probably account for the poor agreement. It is also
difficult to measure tsunami elevations in such small-scale models.
Jordaan and Adams modeled the tsunami to a vertical scale of 1:2000;
thus the waves had heights ten times the normal proportion. Even with
this distortion, waves had heights of only approximately 0.3 millimetres
in the model. The great expense required to build a hydraulic model of
even a small island at a reasonable scale makes hydraulic models
22
unattractive relative to numerical models for most tsunami modeling.
41. Hydraulic models are sometimes useful in modeling complex
tsunami propagation in small regions. For example, the 1960 tsunami
at Hilo, Hawaii, formed a borelike wave in Hilo Bay. In addition, a
phenomenon analogous to the Mach-reflection in acoustics may have de-
veloped along the cliffs north of the city (Wiegel, 1964). A Mach-stem
wave may have entered Hilo and superposed upon an incident wave that came
over and around the Hilo breakwater. Such complicated interactions in-
volving borelike waves would be difficult to model numerically. However,
hydraulic models have been successfully used to model the 1960 tsunami
in Hilo Bay (Wiegel, 1964; Palmer et al., 1964).
42. In general, hydraulic models are not suitable for modeling
tsunami propagation even within small regions. Typical tsunami wave-
lengths (except perhaps when borelike waves are formed) are so long that
wave makers in a hydraulic model are only a small fraction of a wave-
length from the region to be studied. Thus, waves reflected by land are
almost immediately reflected off the wave makers and back into the basin.
Wave absorber screens in front of the wave makers are not very helpful
because it is very difficult to absorb very long waves. The wave makers
can be moved a few wavelengths from the region of interest by reducing
the model scale; however, scale effects then become very significant.
Hydraulic model tests by Grace (1969) suffered the problem of trapping
of wave energy between the wave makers and the shoreline.
Analytical Methods
43. Analytical solutions have long been used to study tsunamis.
They are useful for simplified conditions (e.g., linear bottom slopes)
rather than for general and arbitrary conditions. Analytical solutions
for tsunami interactions with simple bathymetries are often used to
verify numerical model solutions. For example, Omer and Hall's solution
(1949) for the diffraction pattern for long-wave scattering off a
circular cylinder in water of constant depth can be used to verify a
numerical model that calculates the interaction of tsunamis with an
23
island in a constant depth ocean. Hom-ma's solution (1950) for the dif-
fraction pattern for long-wave scattering off a circular cylinder sur-
rounded by a parabolic bathymetry can be used to verify a numerical
model that calculates the interaction of tsunamis with an island in a
variable depth ocean. Analytical solutions also can provide insight
into the important processes determining tsunami propagation. For ex-
ample, Hammack and Segur (1978) used analytical solutions to provide
criteria for the modeling of tsunami propagation.
44. Analytical solutions are often used in engineering practice
to determine tsunami modification during propagation over simple
bathymetric variations or interaction with simple shoreline configura-
tions. Camfield (in preparation) presented a description of many of the
analytical solutions that have been used in engineering piactice. These
solutions are useful when time or cost constraints rule out application
of more general numerical models.
h5. There are problems associated with use of analytical solutions
to determine tsunami propagation for actual arbitrary conditions.
Different phenomena, such as refraction, diffraction, shoaling, reflec-
tion, and runup, usually must all be solved separately if analytical
solutions are used. There are many techniques used to solve each of
these processes. The techniques often make different simplifying assump-
tions and provide different answers. For example, Camfield (in
preparation) discussed several formulas that have been used to calculate
tsunami runup. Some traditional techniques, such as simple refraction
methods, also have been shown to be inadequate for most tsunami propaga-
tion problems (Jonsson et al., 1976).
Numerical Models
Generation anddeep ocean propagation
h6. Numerical models have been developed to generate tsunamis and
to propagate them across the deep ocean (Hwang et al., 1972; Chen, 1973;
Garcia, 1976). These models use finite difference methods to solve the
24
linear long-wave equations on a spherical coordinate grid. One of the
models (Hwang et al., 1972) solves a nonlinear continuity equation,
since the total water depth including the tsunami height is used. How-
ever, the tsunami height is so small compared with the water depth that
this nonlinearity is inconsequential (and requires additional computa-
tional time). These models employ grids covering large sections of the
Pacific Ocean. Transmission boundary conditions are used on open
boundaries to allow waves to escape from the grid instead of reflecting
back into the region of computation. Two of the models (Chen, 1972;
Garcia, 1976) solve the equations of motion with an explicit formulation.
The model of Hwang et al. uses an implicit-explicit formulation devel-
oped by Leendertse (1967) and the transmission boundary condition that
requires the time step employed in the calculations be limited by the
stability constraint for explicit formulations. However, the implicit-
explicit formulation requires more computational time than required by
explicit formulations when the time step is limited by the same
stability constraint.
4 7. These generation and deep-ocean propagation models use an
initial condition that an uplift of water surface in the source region
is identical to the permanent vertical ground displacement produced by
the tsunamigenic earthquake. Hammack (1972) demonstrated that it is
this permanent vertical ground displacement, and not the transient
motions that occur during the earthquake, that determines the far-field
characteristics of the resulting tsunami. In addition, Hammack showed
that the small-scale details of the permanent ground deformation pro-
duce waves that are not significant far from the source region. Thus,
distantly generated tsunamis can be studied only knowing the major
features of the permanent ground deformation.
48. Hwang et al. (1972) used data of the permanent vertical ground
displacement of the 1964 Alaskan tsunami collected by Plafker (1964) in
a simulation of the 1964 tsunami. Good agreement was demonstrated by
Hwang et al. between a recording of the 1964 tsunami (Van Dorn, 1970) in
relatively deep water off the coast of Wake Island and a simulation of
this tsunami using a numerical model. Houston (1978) used the model of
P-5
Hwang et al. and the model of Garcia (1976) to generate the 1964 Alaskan
and the 1960 Chilean tsunami, respectively. The data of the permanent
vertical ground displacement of the 1964 and 1960 earthquakes collected
by Plafker (1964) and Plafker and Savage (1970) were used as initial
conditions in these models. The deepwater wave forms calculated by
these models were used by Houston (1978) as input to a nearshore numeri-
cal model covering the Hawaiian Islands. Good agreement was shown be-
tween tide gage recordings of these tsunamis in the Hawaiian Islands
and the numerical model calculations. Houston and Garcia (1977) showed
similar comparisons between tide gage recordings of the 1964 Alaskan
tsunami on the west coast of the United States and numerical model
calculations.
Tsunami interaction with islands
49. Tsunami destruction in the Hawaiian Islands has directed in-
terest toward the development of numerical models to simulate the inter-
action of tsunamis with islands. Several numerical models have been
developed in recent years. All of these models solve the linear long-
wave equations, but different techniques are used in the solutions;
therefore, the models have different capabilities.
50. Vastano and Reid (1967) developed a numerical model to study
the problem of determining the interaction of monochromatic plane waves
of a tsunami period with a single island. A transformation of coordi-
nates allowed a mapping of the arbitrary shoreline of an island into a
circle in the image plane. The finite difference solution employed a
grid that allowed greater resolution in the vicinity of the island
than in the deep ocean. Such a variable grid is important since islands
are usually small and surrounded by a very rapidly varying bathymetry.
This numerical model can be applied only to a single island and not a
multiple-island system.
51. Vastano and Bernard (1973) extended the techniques developed
by Vastano and Reid (1967) to multiple-island systems. However, the
transformation of coordinates technique allows high resolution only in
the vicinity of one island of a multiple-island system. Thus, when
Vastano and Bernard applied their model to the three-island system of
26
Kauai, Oahu, and Niihau in the Hawaiian Islands, the two islands of Oahu
and Niihau had to be represented by cylinders with vertical walls whose
cross sections were truncated wedges. Kauai was represented by a circu-
lar cylinder with the surrounding bathymetry increasing linearly in
depth with distance radially from the island until a constant depth was
attained. A single Gaussian-shaped plane wave composed of a broad band
of wave frequencies was used as input to the model. No comparisons were
made with historical tsunami data for the three islands. The model does
allow the approximate effects of neighboring islands on a primary island
4of interest to be included in the calculations.
52. A finite difference model employing a grid covering the
Hawaiian Island chain was used by Bernard and Vastano (1977) to study the
interaction of a plane Gaussian pulse with the islands. The square grid
cells were 5.5 km on a side and close to the minimum feasible size for
a constant-cell finite difference grid covering the major islands of
Hawaii. However, historical data indicate that significant variations of
tsunami elevations occur over distances much less than 5.5 km. The
islands of Hawaii are relatively small and not well represented by a
5.5-km grid. For example, Oahu has a diameter of only approximately
30 km, and the land-water boundary of the island has characteristic
direction changes that occur over distances of much less than 5.5 km.
The offshore bathymetry of the islands also varies rapidly with depth
changes of more than 1500 m frequently occurring over distances of 5.5 km.
Furthermore, if a resolution of eight grid cells per wavelength is main-
tained for tsunami periods as low as 15 min, a 5.5-km grid cannot be
used for depths much below 300 m. However, the processes that cause
significant modifications and rapid variations of elevations along the
coastline, which are known to occur during historical tsunamis, probably
occur in this region extending from water at a depth of 300 m to the
shoreline. This model allows all the islands of a multiple-island system
to be included in the calculations and can determine the interaction of
an arbitrary tsunami with the island system.
53. Lautenbacher (1970) developed a numerical model that solved an
integral equation. He applied it to an island with slopixig sides
27
surrounded by a constant depth ocean. An advantage of the model is that
a wall or "no flow" condition is not required at the shoreline. However,
the computational requirements of the model are extremely large since
the matrix to be inverted is full. Thus, it is not feasible to apply
the model to determine the interaction of tsunamis with actual islands
surrounded by complex bathymetries. In addition, Mei (1979) demonstrated
that the integral equation method can have eigensolutions at certain
frequencies and lead to ill-conditioned matrices.
54. A finite element numerical model based upon a model developed
by Chen and Mei (1974) for harbor oscillation studies was used by
Houston (1978) to calculate the interaction of tsunamis with the Hawaiian
Islands. The model employed a finite element grid that telescoped from
a large cell size in the deep ocean to a very small size in shallow
coastal waters. The grid covered a region that included the eight major
islands of the Hawaiian Islands. Although time periodic motion was
assumed in the solution, the interaction of an arbitrary tsunami wave
form with the islands was easily determined within the framework of a
linear theory by superposition. Houston also demonstrated good agreement
(major waves) between tide gage recordings of the 1960 Chilean and 1964
Alaskan tsunamis in the Hawaiian Islands and the numerical model simula-
tions of these tsunamis. A generation and deep-ocean propagation numeri-
cal model was used to determine deep-ocean wave forms for these two
tsunamis. These wave forms were used as input to the finite element
numerical model. The advantages of this model include the flexibility
of the finite element method that allows a telescoping grid so that
extremely small elements can be placed in the nearshore region and the
very small computational time required by the model as a result of the
very tight bandedness of the matrix that is inverted. The model cannot
be used to calculate the effects of local tsunamis generated within the
Hawaiian Islands.
55. A time-stepping finite element numerical model developed by
Sklarz et al. (1978) has been used to investigate locally generated
tsunamis near the big island of Hawaii. Large, locally generated
tsunamis occurred on the southeast side of the island of Hawaii in 1868
28
and 1975. Sklarz et al. attempted to simulate the 1975 tsunami by using
a 5-ft uplift of the water surface in an elliptical area off the coast
of the island of Hawaii as an initial condition in their numerical
model. The finite element model solves the linear long-wave equations.
Reasonable general agreement was demonstrated between the numerical
model calculations multiplied by a factor of 4 and measurements of runup
for the 1975 tsunami. Sklarz et al. also claimed that a factor of 4
will account for the difference between the infinite wall at the shore-
line used in their model and the amplification of a tsunami as it moves
from the shoreline to the level of ultimate runup. The advantage of
this model is that the flexibility of the finite element grid allows the
shape of a land mass and a complex offshore bathymetry to be well repre-
sented. It is unlikely that it would be practical to include all of the
Hawaiian Islands in detail in a grid used by this numerical model because
a large matrix must be inverted at each time step. Thus, the cost of
running the model for a large grid would be prohibitive. However,
locally generated tsunamis have historically been important only on the
single island nearest the uplift generating the tsunami; thus, a grid
containing a single island can be used to provide the information of
practical concern for locally generated tsunamis.
Tsunami interaction with coastlines
56. Numerical models have been developed to calculate tsunami
interaction with continental (or large islands such as the Japanese
Islands) coastlines. Many of these models solve long-wave equations.
Some of the models solve long-wave equations that include nonlinear
advective and dissipative terms, and others solve the linear long-vave
equations. According to Hammack and Segur (1978), Goring (1978), dnd
Tuck (1979), the propagation of large (long-period) tsunamis (at least
the initial major waves), such as the 1964 Alaskan tsunami, from the
deep ocean up onto the continental shelf is governed by the linear long-
wave equations. Nonlinear and frequency dispersive effects are not im-
portant during this propagation since the transition from the deep ocean
to the continental shelf occurs over such a short distance that there
is not sufficient time for these effects to become significant. However,
29
these terms may become important during propagation from the edge of
the continental shelf to the shoreline. The linear long-wave equations
may govern tsunami interactions with islands (neglecting effects of reefs
and occasional formation of bores) as a result of the very short shelf
region of small islands in the Pacific Ocean.
57. One-dimensional numerical models that solve nonlinear equations
and include frequency dispersion effects have been developed. Heitner
and Housner (1970) developed a one-dimensional finite element model that
was used to calculate the runup of a solitary wave propagating up a
linear slope. Mader (1974) used a one-dimensional model to calculate
the propagation of solitary waves and sinusoidal wave trains up linear
slopes and past submerged barriers. Garcia (1972) used a one-dimensional
model to study short-period tsunamis that might be generated by horizon-
tal motions of the Mendocino Escarpment off the western coast of the
United States. These one-dimensional models are useful since they pro-
vide insight into the interaction of tsunamis with simple models of con-
tinental slopes. However, two-dimensional models are necessary to
calculate tsunami propagation over realistic bathymetries and interaction
with complex coastlines.
58. Aida (1969) developed a two-dimensional finite difference
numerical model with an explicit formulation to study tsunamis generated
just off the coast of Japan. Various permanent vertical ground displace-
ments for the 1964 Niigata and the 1968 Tokachi-oki tsunamis were used as
initial conditions for this model that solved the linear long-wave equa-
tions. More recently Aida (1978) applied a similar model to investigate
tsunami generation and propagation for five tsunamis generated off the
coast of Japan. A telescoping finite difference grid was used so that
grid cells could be made smaller in selected bays where there were his-
torical measurements of these tsunamis. The tsunami source used in the
calculations was a vertical displacement of the sea bottom derived from
a seismic fault model for each earthquake. A crude general agreement
was shown between the numerical model calculations and the historical
tide gage recordings of the simulated tsunamis. Differences between the
recorded and measured tsunamis are probably largely due to inaccuracies
30
in the seismic fault model used to determine the vertical displacement
of the sea bottom.
59. Houston and Garcia (1978) employed a two-dimensional finite
difference numerical model based upon the original formulation of a
tidal hydraulic numerical model by Leendertse (1967) to study tsunami
interaction with the west coast of the United States. This model solves
long-wave equations that include nonlinear and bottom friction terms.
Leendertse's implicit-explicit multioperational method is employed in
solving these equations. To verify the model, a generation and deep-
ocean propagation numerical model (Hwang et al., 1972) was used to
generate the 1964 Alaskan tsunami and propagate it to the west coast of
the United States. The resulting wave form was used as input to this
nearshore numerical model that propagated the tsunami to the shoreline.
Good agreement was shown between tide gage recordings of the 1964 Alaskan
tsunami at Crescent City and Avila Beach, California, and the numerical
model calculations. This numerical model does not employ a telescoping
grid. However, the time step used by the model is not restricted by
the stability critera for an explicit model. Therefore, it is practical
to use fine grid cells and a grid covering a large area since a fairly
large time step can be employed.
60. A time-stepping, two-dimensional finite element numerical
model has been recently developed by Kawahara et al. (1978). Unlike
most finite element models that are implicit and require costly matrix
inversions at each time step, this model uses a two-step explicit formula-
tion. Thus, the computational time requirements of the model are modest
and would compare favorably with explicit finite difference models. Al-
though the finite difference formulation used by Houston and Garcia
(1978) allows a much larger time step than that permitted by this model,
the flexibility of the finite element grid allows a region to be covered
by fewer cells (as a result of the telescoping properties of the grid)
and permits the shape of coastlines to be well represented. The model
solves the linear long-wave equations in deep water and the long-wave
equations including nonlinear advective terms in shallower water. A
simulation of the 1968 Tokachi-oki tsunami is also performed by
31
Kawahara et al. A crude general agreement between tide gage recordings
of this tsunami and the numerical model calculations are shown (with
differences probably attributable to lack of knowledge concerning the
ground displacement that generated the tsunami).
61. Chen et al. (1978) developed a two-dimensional finite differ-
ence model that solves Boussinesq-type equations. These higher order
equations include the effects of the nonlinear advective terms and
frequency dispersion. Furthermore, Chen et al. found that the third-
order term accounting for frequency dispersion produced spurious high-
frequency components that caused numerical difficulties. Thus, numerical
filtering had to be used to suppress these components. The model was
used to simulate a nearshore tsunami off the coast of Diablo Canyon,
California. Chen et al. also showed that a numerical model solving
long-wave equations including nonlinear terms calculated a tsunami wave
form almost identical (slightly greater amplitudes) to the wave form
calculated by the model that solved the Boussinesq equations. Thus,
frequency dispersion did not produce any significant effects, and
Boussinesq equations were not found superior to long-wave equations.
The slightly lower amplitudes calculated by the model that solved
Boussinesq equations may have been caused by the numerical filtering
that would tend to reduce amplitudes.
Tsunami inundation
62. The final phase of tsunami propagation involves the inundation
of previously dry land. As discussed earlier, inundation patterns are
often fairly simple. The tsunami appears as a rapidly rising water
level, and inland flooding reaches an elevation similar to the tsunami
elevation at the shoreline. However, flow divergence and convergence
resulting from two-dimensional variations in topography (e.g., a narrow-
ing canyon), frictional effects, and time-dependent effects (that can
limit the time available for complete flooding) can change this simple
pattern of inundation. Numerical models are required to determine inun-
dation lines for actual tsunami propagation over complex topography.
63. Bretschneider and Wybro (1976) developed a one-dimensional
model to calculate tsunami inundation. Frictional effects but not
32
time-dependent effects were included in the model calculations. Calcula-
tions can be performed for a series of linear ground slopes. This model
is easy to apply and very economical. The main limitations of this
approach are the one-dimensional and time-independent properties of the
solution in addition to an assumption that the height of the tsunami
decreases with the square of the velocity of the tsunami. This last
assumption appears to contradict laboratory experiments performed by
Cross (1966).
6h. Houston and Butler (1979) described a two-dimensional and
time-dependent numerical model that calculates land inundation of a
tsunami. The model solves lonC-wave equations that include bottom fric-
tion terms. A coordinate transformation was used to allow the model to
employ a smoothly varying grid that permits cells to be small in the
inundation region and large in the ocean. The transformation is a
piecewise reversible transformation (analogous to that used by Wanstrath,
1976) that is used independently in the x and y directions to map the
variable grid into a uniform grid for the computational space. A
variable grid in real space is necessary since the extent of inundation
has a spatial scale much smaller than a tsunami wavelength. An implicit
formulation developed by Butler (1978) is used in the finite difference
model. The model was verified by simulating the 196 4 Alaskan tsunami
at Crescent City, California. This tsunami was very large at Crescent
City (20 ft above mllw), and the Crescent City area is very complex.
For example, Crescent City harbor is protected by breakwaters, some of
which were overtopped and others which were not. There is a developed
city area, mud flats, and an extensive riverine floodplain. Inland
flooding was widespread in the floodplain area and extended as much as a
mile inland. Sand dunes and elevated roads played a prominent role in
limiting flooding in certain areas. Good agreement was demonstrated
between historical measurements (Magoon, 1965) and numerical model calcu-
lations for high-water marks, contours of tsunami elevations above the
land during propagation over previously dry land, and the extent of
inundation.
33
PART IV: TSUNAMI ELEVATION PREDICTIONS
Predictions Based upon Historical Data
65. There are locations in the United States, such as Hilo, Hawaii,
that have sufficient historical data of tsunami activity to allow reason-
able tsunami elevation predictions to be made based upon the available
historical data. For such locations, the historical data can be ranked
from the largest to the smallest recorded elevation (largest elevation
with a rank equal to 1 and the second largest elevation with a rank of 2).
By dividing the rank by the total number of years of record plus one
year, the frequency of occurrence of elevations equaling or exceeding
a recorded elevation (mean exceedance frequency) can be defined.
66. Cox (1964) found that the logarithm of the tsunami mean exceed-
ance frequency was linearly related to tsunami elevations for the ten
largest tsunamis occurring from 1837 to 1964 in Hilo, Hawaii. Earthquake
intensity and the mean exceedance frequency have been similarly related
by Gutenburg and Richter (1965). Furthermore, Wiegel (1965) found the
same relationship between tsunami frequency of occurrence and measured
elevations for tsunamis at Hilo, Hawaii; San Francisco, California; and
Crescent City, California; and Adams (1970), for tsunamis at Kahuku
Point, Oahu. Rascon and Villarreal (1975) demonstrated that a linear
relationship between the logarithm of the mean exceedance frequency and
recorded elevations held for historical tsunamis on the west coast of
Mexico (data from 1732) and on the Pacific West Coast of America, ex-
cluding Mexico. Cox showed that this linear relationship between the
logarithm of the mean exceedance frequency and tsunami elevations at Hilo
was valid for mean exceedance frequencies as high as approximately 0.1
per year (1-in-10-year tsunami) and that the relationship between mean
exceedance frequency and elevation followed a power law for higher fre-
quencies. Thus, the logarithmic distribution may not hold for small
tsunamis. This distribution also must be invalid at some large tsunami
elevation, since earthquakes reach certain maximum elevations as a result
of the upper limit to the strain that can be supported by rock before
34
fracture (Gutenberg and Richter, 1965). Thus, tsunamis can be expected
to have similar upper limits of intensity. The logarithmic distribution
should be adequate (provided there is a sufficient length of historical
record) to determine tsunami hazards at locations other than the sites
of critical facilities such as nuclear power plants. At the site of a
critical facility, the Probable Maximum Tsunami (U. S. Nuclear Regulatory
Commission, 1977) must be predicted by deterministic and not probabilis-
tic methods. Houston et al. (1975) demonstrate this type of determinis-
tic method.
67. Other mean exceedance frequency distributions can be applied
to historical data of tsunami elevations. For example, the Gumbel
distribution has been used in the past to study annual stream-flow
extremes (1955). Borgman and Resio (1977) illustrated the use of this
distribution to determine frequency curves for nonannual events in wave
climatology. If the approach of Borgman and Resio is applied to the
historical data of tsunami activity in Hilo, Hawaii (as compiled by Cox,
(1964)), a 1-in-100-year elevation of 28.8 ft is obtained. This compares
with a 1-in-100-year elevation of 27.3 ft obtained using a logarithmic
distribution. The frequency distribution governing tsunami activity at
a location is not known a priori, and there is not sufficient historical
data to determine a posteriori the governing distribution. However, the
logarithmic distribution has been shown to provide a reasonable fit of
historical data at several locations in the Pacific Ocean region.
68. Historical data of tsunami activity in the United States are
available from several published sources. Iida et al. (1967) and
Soloviev and Go (1969) presented catalogs of tsunami activity in the
Pacific Ocean. Heck (1947) listed the worldwide tsunamis covering the
period from 479 BC to 1946 AD. Beringhausen (1962, 1964) compiled a
catalog of tsunamis in the Atlantic Ocean and also a separate catalog
of tsunamis reported from the west coast of South America (tsunamis
generated in this region are of concern to areas in the United States).
Pararas-Carayannis (1978) published a catalog of tsunami activity in
Hawaii, and Cox and Pararas-Carayannis (1976) a catalog of tsunami
activity in Alaska. Cox and Morgan (1977) described locally generated
35
tsunamis in the Hawaiian Islands.
69. Detailed accounts of several major tsunamis in the United
States are available. For Hawaii, Shepard et al. (1950) described the
1946 tsunami; MacDonald and Wentworth (1954), the 1952 tsunami; Fraser
et al. (1959), the 1957 tsunami; Eaton et al. (1964) and USAE District,
Honolulu (1962), the 1960 tsunami; and Loomis (1976), the 1975 tsunami.
Wilson and Torum (1968), Brown (1964), and Berg et al. (1970) discussed
the 1964 Alaskan tsunami. Magoon (1965) presented the effects of the
1960 and 1964 tsunamis in northern California. Reid and Taber (1919,
1920) discussed the 1868 tsunami in the Virgin Island and the 1918
tsunami in Puerto Rico. Keys (1963) described the 1960 tsunami in Ameri-
can Samoa. Symons and Zetler (1960) and Spaeth and Berkman (1967) pre-
sented tide gage recordings in the Pacific Ocean region of the 1960 and
196h tsunamis. Tide gage records of several historical tsun1amis in the
Pacific Ocean are available from the World Data Center A for Solid Earth
Geophysics, National Oceanographic and Atmospheric Administration,
Boulder, Colorado.
Predictions Based upon Historical Dataand Numerical Models
Introduction
70. Most of the coastline of the United States has little or no
data of tsunami activity. For example, most of the west coast of the*
United States has no quantitative data of tsunami elevations. Only a
very few locations have data for tsunamis other than the 1964 Alaskan'
tsunami. The Hawaiian Islands have substantial data of tsunami eleva-
tions for tsunamis since 1946. However, the historical observations
since 1946 are at discrete locations; therefore, elevations are not known
along many stretches of coastline. :ata of tsunami activity since 1837
is available in the Hawaiian Islands; however, historical observations
prior to 1946 are concentrated in Hilo, Hawaii.
71. In addition to the general scarcity of historical data, data
that are available are for recent years when tsunami activity has appar-
ently been greater than the long-term trend. For example, in Hilo,
36
Hawaii, the two largest and four of the ten largest tsunamis striking
Hilo from 1837 through 1979 occurred during the 15-year period from
1946 through 1960. Two of the tsunamis from 1946 through 1960 originated
in the Aleutian Islands, one in Kamchatka, and one in Chile. However,
six of the ten largest tsunamis occurred during the 109-year period from
1837 through 1945 with three originating in Chile, two in Kamchatka, and
one in Hawaii. Thereforc, both the frequency of occurrence and place of
origin of tsunamis have been remarkably variable. The exceptionally
frequent occurrence of major tsunamis in Hilo, Hawaii, during the period
from 1946 to 1960 is a property of the unusual activity of tsunami
generation areas and not of special properties of Hilo. Thus, any
analysis of tsunami activity that uses a short time span that includes
the period from 1946 through 1960 will predict a significantly more
frequent occurrence of large tsunamis than is warranted by historical
data from 1837 through 1979.
72. From an analysis of tsunami data for Hilo, Hawaii, the errors
introduced in frequency-of-occurrence calculations by consideration of
a short period that includes the unrepresentative years from 1946 through
1960 are apparent. A l-in-100-year elevation for Hilo, based upon
data compiled by Cox (1964) for the ten largest tsunamis in Hilo from
1837 through 1976 and assuming a logarithmic distribution, is 27.3 ft.
The l-in-100-year elevation that is based just upon the large tsunamis
during the period of accurate survey measurements in Hilo from 1946
through 1976 is 44.2 ft. Since the largest elevation in Cox's data
for the 140-year period from 1837 through 1976 was 28 ft (1960 Chilean
tsunami), the 44.2-ft elevation for a l-in-100-year tsunamis is obviously
much too large. The choice of frequency distributions does not change
this conclusion. For example, use of a Gumbel distribution yields a
l-in-100-year elevation of 42.5 ft if the analysis is just based upon
data since 1946. Of course, the quantitative accuracy of the data for
tsunamis in Hilo from 1837 through 1945 may be somewhat questionable.
However, there is little doubt that the recorded occurrence of large
tsunamis is accurate (i.e., tsunamis noted as being significant were in-
deed so, and major tsunamis did not occur and go unrecorded). In
37
addition, errors introduced by consideration of a short period that
includes the years from 1946 through 1960 are greater than the errors
resulting from possible observational inaccuracies of the 19th century
in Hilo. For example, increasing by 50 percent the reported elevations
for the five largest tsunamis recorded in Hilo Ql-ing the 19th century
(these five are included in the ten largest tsunamis recorded in Hilo)
yields a l-in-100-year elevation of 30.4 ft. This elevation is similar
to the 27.3-ft elevation obtained using the reported elevations for the
five largest tsunamis recorded during the 19th century.
73. The lack of historical data of tsunami activity in the
United States covering reasonable periods of time makes it necessary
to use various methods to expand the data base. For example, Rascon
and Villarreal (1975) predicted elevations at a site in Mexico by using
historical data collected for the entire west coast of Mexico. A fre-
quency distribution based upon data recorded at Hilo, Hawaii, and a
Bayes estimation procedure are used to improve the estimate based upon
the data for the west coast of Mexico. Such an approach is questionable
since tsunamis at Hilo are primarily generated locally, in Kamchatka,
in Chile, and in Alaska, whereas the tsunamis recorded on the west coast
of Mexico are primarily locally generated. Therefore, there is no rea-
son that the frequency distribution in Hilo should be related to the
distribution for the west coast of Mexico. In addition, elevation pre-
dictions for the specific site in Mexico are not based upon local ef-
fects that may amplify the tsunami. The following two sections describe
studies that employ various techniques, including the use of numerical
models to expand the data base, and thus allow elevation predictions
at arbitrary locations within the study region.
Predictions for
the Hawaiian Islands
74. Houston et al. (1977) described in detail methods used to make
tsunami elevation frequency of occurrence predictions for the Hawaiian
Islands. In order to make these predictions it was necessary to use
data of tsunami activity in Hilo, Hawaii, to expand the data base at
locations having recorded data of tsunami activity since 1946. In
38
I /
I
addition, Houston et al. used a numerical model to aid in developing
predictions at locations not having complete data for tsunamis since
1946 or not having any data at all of tsunami activity.
75. To reconstruct elevations prior to 1946 at locations having
historical data since 1946, Houston et al. (1977) noted that tsunamis
originating near the Aleutian Islands, Kamchatka, and Chile were re-
corded in the Hawaiian Islands from 1946 to 1964. Therefore, the re-
sponse is known of many areas in the Hawaiian Islands to tsunamis origi-
nating in the three main locations where tsunamis of destructive power
in these islands have historically been generated. Houston et al.
assumed that tsunamis generated in a single source region (Kamchatka or
Chile, but not the Aleutians) approach the islands from approximately
the same direction and have energy lying in the same band of wave
periods. The difference in wave elevations at the shoreline in the
Hawaiian Islands produced by tsunamis generated at different times in
the same region was attributed mainly to differences in deepwater wave
amplitudes. For example, the 1841 tsunami from Kamchatka produced a
wave elevation in Hilo, Hawaii, that was approximately 25 percent
greater than that of the 1952 tsunami from Kamchatka. The same relative
magnitudes of the two tsunamis were used for all of the islands to deter-
mine the elevation that must have occurred in 1841 at some location,
knowing the elevation that did occur in 1952. Therefore, knowing the
elevations of tsunamis from 1946 to 1960 at a location and the response
of Hilo to tsunamis from 1837 to 1960 allowed a reconstruction of the
elevations that occurred prior to 1946 at the location but were not re-
corded (for tsunamis from Chile and Kamchatka). Data from 1837 at Hilo
were used instead of data from 1837 at Honolulu (Hilo and Honolulu are
the only two locations with substantial data since 1837) since data do
not exist at Honolulu for the 1868 and 1877 tsunamis, and the 1837 and
1841 elevations given by Pararas-Carayannis (1978) were drops in the
water level and not runup elevations.
76. The assumption that tsunamis generated in Kamchatka and Chile
approach the Hawaiian Islands from nearly the same direction was justi-
fied by Houston et al. (1977) by the small spatial extent of the known
39
mom
generation areas in Kamchatka and a study of tsunami propagation from
Chile by Garcia (1976) that indicated that directional effects for
tsunamis originating along the Chilean coast are small in the Hawaiian
Islands (probably because the generation areas in Chile subtend a rela-
tively small angle with respect to the Hawaiian Islands). The position
of the Aleutian-Alaskan Trench relative to the Hawaiian Tslands does in-
troduce important directional efforts for tsunamis generated in the
Aleutian-Alaskan area. However, these effects are known from historical
observations for tsunamis generEoted in the western Aleutians (1957),
central Aleutians (1946), and eastern Alaskan area (1964).
77. Historical observations of tsunamis in Hawaii support the
approach by Houston et al. (1977) that estimates the elevations produced
by tsunamis from Chile or Kamchatka prior to 1946 based upon data for
tsunamis from these tsunamigenic regions recorded during the years of
accurate survey measurements since 1946. Eaton et al. (1964) noted that
in the Hawaiian Islands "Tsunamis of diverse geographic origin are strik-
ingly different, whereas those from nearly the same origin are remarkably
similar." Wybro (in preparation) showed that even the distributions of
normalized elevations (elevations normalized by the largest recorded
elevation) produced in the Hawaiian Islands by different Aleutian-Alaskan
tsunamis are nearly the same yet quite different from the distributions
for tsunamis of other origins. Therefore, it is a reasonable assumption
that tsunamis from the same geographic origin produce similar runup
patterns in the Hawaiian Islands. Thus, the elevation of a pre-1946
tsunami at a location that has a recorded elevation for a post-1946
tsunami from the same geographic origin can be estimated using the ratio
of recorded elevations of both tsunamis at Hilo, Hawaii.
78. There are many locations in the Hawaiian Islands that do not
have recordings of tsunami elevations since 1946 or only have recordings
of some of these tsunamis. To reconstruct elevations at these locations,
Houston et al. (1977) used a finite element numerical model covering all
of the Hawaiian Islands to simulate tsunami interactions with these
islands. The numerical model calculations were then used to interpolate
between recorded elevations and predict elevations at locations lacking
40
historical observations. The finite element model and the verification
simulations of actual historical tsunamis in the Hawaiian Islands are
described by Houston (1978). The numerical model calculations allow
predictions of the elevations of tsunamis since 1946 to be made at any
location in the Hawaiian Islands. The historical record at Hilo,
Hawaii, can then be used to reconstruct elevations for tsunamis prior to
1946. Thus, a record of tsunami activity dating back to 1837 (beginning
of Hilo record) can be reconstructed at any location and frequency of
occurrence curves determined. Houston et al. (1977) presented fre-
quency of occurrence curves for all of the coastline of the Hawaiian
Islands.
Predictions for the westcoast of the United States
79. Unlike the Hawaiian Islands, the west coast of the continental
United States lacks sufficient data to allow tsunami elevation predic-
tions to be made based upon local historical records of tsunami activity.
Virtually all of the west coast is completely without data of tsunami
occurrence, even for the prominent tsunami of 1964. Only a handful
of locations have historical data for tsunamis other than the 1964
tsunami.
80. The lack of historical data of tsunami activity on the west
coast of the United States necessitates the use of numerical models to
predict runup elevations. Brandsma et al. (1977) used a deep-ocean
numerical model to predict probable maximum tsunami wave forms in
water depths of 600 ft off the west coast of the United States.
Houston and Garcia (1974) used a numerical model to predict tsunami
elevations in the southern California region; Garcia and Houston (1975),
numerical models to predict tsunami elevations in Puget Sound, San
Francisco Bay, and Monterey Bay; and Houston and Garcia (1978), numerical
models to predict tsunami elevations on all of the west coast of the
United States outside of these regions.
81. In order to predict tsunami elevations on the west coast of
the United States, it is necessary to base the analysis on historical
data of tsunami generation in the tsunamigenic regions of the Pacific
41
Ocean of concern to the west coast. Houston and Garcia (1974) showed
that the Aleutian-Alaskan area and the west coast of South America are
the tsunamigenic regions of concern to the west coast. These regions
have sufficient data on the generation of major tsunamis to allow a
statistical investigation of tsunami generation. It is necessary to use
historical data of tsunami occurrence in generation regions to determine
occurrence probabilities of tsunamis rather than using data of earth-
quake occurrence to predict tsunami occurrence. Earthquake occurrence
statistics are of little value since a satisfactory correlation between
earthquake magnitude and tsunami intensity has never been demonstrated.
Not all large earthquakes occurring in the ocean even generate notice-
able tsunamis. Furthermore, earthquake parameters of importance to
tsunami generation, such as focal depth, rise time, and vertical ground
motion, have only been measured for earthquakes occurring in recent
years.
82. Houston and Garcia (1978) used the most recent and complete
catalog (Soloviev and Go, 1969) of tsunami occurrence in the Pacific
Ocean to determine relationships between tsunami intensity and frequency
of occurrence for the Aleutian-Alaskan and South American regions. The
tsunami intensity scale used in the analysis is a modification by
Soloviev and Go of the standard Imamura-Iida tsunami intensity.
Intensity is defined as
i = log2 (Vr Havg) ()
This definition in terms of an average runup H (in metres) over aavg
coast instead of a maximum runup elevation at a single location (used
for the standard Imamura-lida scale) tends to eliminate any spurious
intensity magnitudes caused by often observed anomalous responses (due,
for example, to local resonances) of single isolated locations. Houston
and Garcia (1978) assumed that the logarithm of the tsunami frequency
of occurrence was linearly related to the tsunami intensity and used
linear regression of the historical data to determine the probability
distributions of tsunami generation for these two tsunamigenic regions.
42
4
83. To relate the probability distributions of different intensity
tsunamis to source characteristics, Houston and Garcia (1978) assumed
that the ratio of the source uplift heights producing two tsunamis of
different intensities (as defined earlier) was equal to the ratio of
the average runup heights produced on the coasts near these tsunami
sources. This ratio is equal to 2(i1-i2) for two tsunamis with inten-
sities i and i2
84. The directional radiation of energy from tsunami source regions
was described in Part II. The strong directional radiation from large
tsunami sources makes the orientation of a tsunami source relative to
a distant site where runup is to be determined very important. Thus,
the runup at a distant site due to the generation of a tsunami at one
location along a trench cannot be considered as being representative of
all possible placements of the tsunami source in the entire trench
region. In order to account for the effects of directional radiation,
Houston and Garcia (1978) segmented the Aleutian and Peru-Chile Trenches
and used a deep-ocean propagation model to generate tsunamis in each of
the segments. The Aleutian Trench was segmented into 12 sections and
the Peru-Chile Trench into 3 sections. The Aleutian Trench was seg-
mented much finer than the Peru-Chile Trench since the Aleutian Trench
is oriented relative to the west coast such that elevations produced on
the west coast are very sensitive to the exact location of a source
along the Trench. For example, the 1946 and 1957 Aleutian tsunamis did
not produce large elevations on the west coast, whereas the 1964 Alaskan
tsunami radiated waves toward the northern part of this coast where
large elevations were recorded. Uplifts along the Peru-Chile Trench
do not radiate energy directly toward the west coast regardless of their
position along the Trench. The Peru and Chile sections of the Peru-
Chile Trench also have constant orientations relative to the west coast
of the United States; therefore, elevations on the west coast of the
United States are relatively insensitive to source location within
these sections.
85. Houston and Garcia (1978) used deep-ocean propagation numeri-
cal models to generate tsunamis with intensities from 2 to 5 in steps of
43
one-half intensity in each of the segments of the two trench regions.
Tsunamis with intensities less than 2 are too small to produce signifi-
cant runup on the west coast. An upper limit of 5 was chosen because
the greatest tsunami intensity ever reported was less than 5 (Soloviev
and Go, 1969). Perkins (1972) and McGarr (1976) demonstrated that
future earthquakes cannot have seismic moments (measure of earthquake
magnitude for large earthquakes) much larger than those of earthquakes
that have occurred in recorded history. Since earthquakes only reach
certain maximum magnitudes, tsunamis can be expected to have similar
upper limits to intensity. The tsunamis generated in the trench regions
were propagated across the deep ocean using the deep-ocean propagation
models.
86. As tsunamis approach the west coast of the United States their
wavelengths decrease as a result of the decreasing water depths. The
numerical grids used by Houston and Garcia (1978) for deep-ocean propaga-
tion have too large a grid cell spacing to properly simulate tsunami
propagation over the continental shelf of the west coast. Houston and
Garcia (1974) used an analytic solution to propagate tsunamis over the
continental shelf to the shoreline. Houston and Garcia (1978) used a
numerical model that solved long-wave equations, including nonlinear and
dissipative terms, and employed a very fine grid to propagate tsunamis
over the continental shelf to the shoreline. Wave forms propagated to
the west coast by the deep-ocean propagation models were the input to
this nearshore numerical model. Each wave form was propagated from a
water depth of 500 metres to shore using the nearshore model. Numerical
simulations of the 1964 tsunami at Crescent City and Avila Beach, Cali-
fornia, were used to verify the numerical model. At each numerical grid
location on the west coast, a group of 105 wave forms were determined by
Houston and Garcia (1978 )--seven wave forms (for intensities from 2 to 5
in one-half intensity increments) for each segment of the Aleutian and
Peru-Chile Trenches. Each of these wave forms had an associated proba-
bility equal to the probability that a certain intensity tsunami would
be generated in a particular segment of a trench region.
87. The maximum "still-water" elevation produced during tsunami
414
.' _U h
activity is the result of a superposition of tsunamis and tides. There-
fore, the statistical effect of the astronomical tides on total tsunami
runup must be included in a predictive scheme. Houston and Garcia (1974)
used an analytical solution to determine combined tsunami and astronomi-
cal tide cumulative probability distributions. Houston and Garcia (1978)
also employed a direct numerical solution similar to that used by
Petrauskas and Borgman (1971) to determine combined tsunami and astronom-
ical tide cumulative probability distributions. It was necessary to
employ a numerical solution since the tsunami wave forms calculated by
Houston and Garcia (1978) using a nearshore numerical model did not have
a simple form (e.g., sinusoidal). Houston et al. (1977) did not need to
consider the effect of the astronomical tides in their elevation predic-
tions for the Hawaiian Islands since the tidal range is quite small for
these islands and the local historical data implicitly contained the ef-
fects of the astronomical tides.
88. In order to perform a convolution of tsunamis and astronomical
tides, Houston and Garcia (1978) calculated tidal elevations for a year
at locations all along the west coast using harmonic analysis methods
(Shureman, 1941). The year was then divided into 15-min segments, and
24-hr tsunami wave forms were allowed to arrive at the beginning of each
of these 15-min segments and then superposed upon the astronomical tide
for the 24-hr period. The maximum combined tsunami and astronomical
tide elevation over the 24-hr period was determined for tsunamis arriving
at each of these 15-min starting times during a year. All of the maximum
elevations had an associated probability equal to the probability that
a certain intensity tsunami would be generated in a particular segment
of the two trench regions and arrive during a particular 15-min period
of a year. These many maximum elevations with associated probabilities
were used by Houston and Garcia (1978) to determine cumulative proba-
bility distributions of combined tsunami and astronomical tide elevations.
The 100- and 500-year elevations were determined for locations along
the west coast of the United States using these cumulative probability
distributions. Elevations for arbitrary return periods can be obtained
by assuming that the 100- and 500-year elevations determined by Houston
45
r/
and Garcia (1978) follow a logarithmic distribution.
Risk Calculation
89. The average frequency of occurrence F calculated by Houston
et al. (1977) and Houston and Garcia (1978) is a mean exceedance fre-
quency, i.e., an average frequency per year of tsunamis occurring and
producing an equal or greater elevation. It also is possible to calcu-
late the chance of a given elevation being exceeded during a particular
period of time. Such a calculation is a risk calculation.
90. Tsunamis are usually caused by earthquakes, and earthquakes
are often idealized as a generalized Poisson process (Newmark and
Rosenblueth, 1971). Many investigators have assumed that tsunamis also
follow a stochastic process (Wiegel, 1965; Rascon and Villarreal, 1975).
The probability that a tsunami with an average frequency of occurrence
of F is exceeded in D years, assuming that tsunamis follow a
Poisson process, is given by the following equation:
P = 1 - e - FD (2)
For example, the probability that a l-in-l00-year elevation will occur
in a 50-year period is
P I - e- (0 .0 1 )(50 )
=1- e-
= 1 - 0.61
= 0.39
Tsunami Hazard Maps
91. Figure 2 is the general tsunami hazard map for the United
States, and Figures 3 through 11 are the detailed maps (Houston et al.,
1977; Houston and Garcia, 1974 and 1978; Garcia and Houston, 1975).
Houston et al. (1977) presented frequency curves of tsunami elevations
46
for the Hawaiian Islands, and Houston and Garcia (1974 and 1978) and
Garcia and Houston (1975) predicted 100- and 500-year elevations for
the west coast of the continental United States. A tsunami elevation
with a 90 percent probability of not being exceeded in 50 years repre-
sents a 475-year elevation. This is easily calculated from the previous
paragraph by setting D = 50 and P = 0.1 (10 percent probability of
being exceeded) and solving for 1/F
4,7
ARCTIC OCEAN
....................,..
BERING SEAZONE 2
(EXCEPT ALEUTIAN ISLANDS) ,LANDSLIDES OR SUBAQUEOUS SLIDES)CAN PRODUCE ZONE 5 ELEVATIONS1
*% (e.g. LITUYA BAY, ALASKA)
ALEUTIAN ISLANDS(SAME AS GULF OF ALASKA)
GULF OF ALASKAZONE 3
(EXCEPT END OF INLETS ANDFJORDS THAT ARE IN ZONE4 AND POSSIBLY ZONE 5)
MAP OF TSUNAMI ELEVATIONS ALASKAN PANHANDLEWITH A 90 PERCENT PROBABILITY AS N POF NOT BEING EXCEEDED IN 50 YEARS ZONE 2(EXCEPT ENDS OF INLETS ANDTHE ELEVATIONS DO NOT INCLUDE FJORDS ON PACIFIC SIDE OFEFFECT OF ASTRONOMICAL TIDES ISLANDS THAT ARE IN ZONE 3)EXCEPT ON PACIFIC COAST ANDHAWAII WHERE COMBINED TSUNAMIAND ASTRONOMICAL TIDE ELEVATIONSARE GIVEN
/ PACIFIC COAST --......---------- " . ...ZONE 2 !' J ;
(EXCEPT FOR ZONE 3 -------J-" ----- ' 0'I
i - 'rAREAS SHOWN ON % ..... %2 ,. )- ...
DETAILED MAPS) , UNITED STATES (. " EAST COAST-\ ". /. ... I _ "lr - ZONE I "
HAWAIIAN ISLANDS "
(SEE DETAILED MAPS) GULF COAST.) ZONE 1 i
ZONE 1 0 TO 5 FT PUERTO RICO AND C=7ZONE 2 5 TO 15 FT VIRGIN ISLANDSZONE 3 15 TO 30 FT ZONE3ZONE 4 30 TO 50 FT (EXCEPT SOUTHERN PUERTOZONE 5 50 FT OR GREATER RICO THAT IS IN ZONE 2)
Figure 2. Tsunami hazard map
48
4t" SI- 4" St
4" tar I
-W
.6WO.,~
, ~' 4 8
27N
57 Iv- W
X* 30N
NN.
19Th~~~~~~~4 and 198 Gacaan oson95
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Figure 4~. Tsunami hazard for Oregon and Washington (adapted fromHouston and Garcia, 1978)
50
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PART V: THE TSUNAMI WARNING SYSTEM
92. Although tsunamis propagate at velocities as great as 500 mph
in the deep ocean, transoceanic distances are sufficiently large to
allow several hours warning before arrival of a distantly generated
tsunami. Thus, given prompt warning of the generation of a tsunami,
there is sufficient time to reduce the potential hazard to life or mobile
equipment (such as ships or automobiles) by evacuation procedures. The
Tsunami Warning System (TWS) was founded in 1946 (following the Aleutian
tsunami of 1 April 1946 that caused major damage and many casualties in
the Hawaiian Islands) by the U. S. Coast and Geodetic Survey to provide
warning in the event of the occurrence of a tsunami. The TWS is cur-
rently operated by the National Weather Service, which is under the
direction of the National Oceanic and Atmospheric Administration of the
U. S. Department of Commerce.
93. The TWS is a cooperative effort among nations bordering
the PacifW Ocean to provide early warning of potentially disastrous
tsunamis. Seismograph and tide data are collected and communicated to
the Pacific Tsunami Warning Center (PTWC) at Ewa Beach, Hawaii, for
analysis and evaluation. If warranted, tsunami watches or warnings are
disseminated immediately by the Center to affected coastal populations
(Spaeth, 1975).
94. The TWS begins functioning with the detection, by any partici-
pating seismic observatory, of an earthquake of sufficient size to
trigger the alarm attached to the seismograph at that station. The
alarm thresholds are set for each station so that the ground vibrations
of the amplitude and duration associated with an earthquake of approxi-
mate magnitude of 6.5 or greater anywhere in the Pacific region will
cause them to sound. This magnitude is below the threshold for issuing
watch and warning messages. Personnel at the station immediately inter-
pret their seismographs and send their readings to the PTWC. Upon re-
ceipt of a report from one of the participating seismic observatories
or as a consequence of the triggering of their own seismic alarm, PTWC
57
•/
personnel send messages requesting data to the observations in the
system (Spaeth, 1975).
95. When sufficient data have been received for PTWC personnel to
locate the earthquake and compute the magnitude, a decision is made as
to further action. If the earthquake is strong enough to cause a tsunami
and is located in an area where tsunami generation is possible, PTWC
personnel will request participating tide stations located near the
epicenter to monitor their gages for evidence of a tsunami. Watch bulle-
tins are issued to the dissemination agencies for earthquakes of magni-
tude 7.5 or greater (7 or greacer in the Aleutian Island region), alert-
ing them to the possibility that a tsunami has been generated and
providing data that can be relayed to the public so necessary prelimi-
nary precautions can be taken. A watch also may be disseminated by the
PTWC upon issuance of warnings by regional warning centers. Since the
regional systems use different criteria for their disseminations, a
watch may at times be issued by the PTWC for earthquakes with magnitudes
less than 7.5 (Spaeth, 1975).
96. When reports are received from tide stations, they are evalu-
ated; if they show that a tsunami has been generated that poses a threat
to the population in part or all of the Pacific, a warning is trans-
mitted to the dissemination agencies for relay to the public. The dis-
semination agencies then implement predetermined plans to evacuate
people from endangered areas. If the tide station reports indicate that
either a negligible tsunami or no tsunami has been generated, PTWC
issues a cancellation of its previously disseminated watch (Spaeth, 1975).
97. Because of the time spent in collecting seismic and tidal data,
the warnings issued by the PTWC cannot protect areas against tsunamis
generated in adjacent waters. For providing some measure of protection
against local tsunamis in the first hour after generation, regional
warning systems have been established in some areas. To function effi-
ciently, these regional systems generally have data from a number of
seismic and tide stations telemetered to a central headquarters. Nearby
earthquakes are located, usually in 15 min or less, and a warning based
on seismological evidence is released to the population of the area.
58
Since the warning is issued on the basis of seismic data alone, one may
anticipate that warnings occasionally will be issued when tsunamis have
not been generated. Since the warnings are issued only to a restricted
area and confirmation of the existence or nonexistence of a tsunami is
obtained rapidly, dislocations due to the higher level of protection are
minimized. Among the most sophisticated of the regional systems are
those of Japan and Alaska. The command center of the Alaska regional
system is the Alaska Tsunami Warning Center in Palmer, Alaska (Spaeth,
1975).
98. Offices of the U. S. Army Corps of Engineers may obtain infor-
mation about tsunami watches and warnings from the U. S. Army Engineer
Division, Pacific Ocean; the U. S. Sixth Army, Presidio, California; or
Civil Defense agencies of Hawaii, California, Oregon, Washington, or
Alaska. These organizations receive all tsunami watch and warning
messages from the PTWC. Tsunami arrival times La the Hawaiian Islands
from tsunamis generated anywhere in the Pacific region can be estimated
by using Figure 12. Tsunami arrival times in Alaska, Hawaii, or the
west coast of the United States for tsunamis generated in the Aleutian
Islands or eastern Alaska can be estimated by using Figures 13 and 14.
The PTWC does not supply predictions of areas in possible danger. How-
ever, elevation predictions by Houston et al. (1977) for the Hawaiian
Islands, Houston and Garcia (1974) for southern California, Garcia and
Houston (1975) for Monterey and San Francisco Bays and Puget Sound,
and Houston and Garcia (1978) for the rest of the west coast of the
United States can be used to determine areas of possible danger. Per-
sonnel should evacuate these areas if there is sufficient time; ships
should depart harbors for the safety of the open seas (tsunami elevations
are very small in the open ocean). Vessels should avoid harbor entrances
or other restricted channels where large currents may develop during
tsunami activity. Vessels also should be moored at locations away from
important facilities if large tsunami elevations are expected since the
vessels may act as projectiles and cause destruction.
59
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62
PART VI: TSUNAMI STRUCTURAL DAMAGE
Introduction
99. Tsunamis can cause great damage to structures. The severe
destruction in Hilo, Hawaii, diring the 1946 and 1960 tsunamis (Shepard
et al., 1950; Reese and Matlock, 1960); in many Alaskan cities during
the 1964 tsunami (Wilson and Torum, 1968); and in Crescent City,
California, during the 1964 tsunami (Wilson and Torum, 1968; Magoon,
1965) is well documented. The tremendous forces developed by tsunamis
are illustrated by the destruction in Seward, Alaska, during the 1964
tsunami. Wilson and Torum reported that a 115-ton locomotive was over-
turned and transported 300 ft by this tsunami. A winch bolted down and
welded to railroad irons set in 6 ft of concrete was torn loose by wave
forces that sheared four pieces of railroad steel. The waves carried
a 26-ton crane 500 ft inland and wrapped a 6-ton panel truck around a
tree.
100. To calculate the force of tsunamis on a structure, it is
necessary to know the speed and direction of flow, as well as the water
level as a function of time. The nature and shape of the structure
are, of course, of basic importance. Tsunamis usually appear as rapidly
rising water levels. Wilson and Torum (1968) showed that for such a
case the speed of the water across land is approximately
2nA (2nt
where
u - horizontal speed, ft/sec
A = tsunami amplitude, ft
T = tsunami period, sec
s = ground slope
t = time, sec
For small ground slopes, the tsunami speed becomes limited by the
63
propagation speed of a bore. This speed is given by the expression
(Wilson and Torum, 1968)
u = C(gd)I /2 (4)
where
C dimensionless number varying between 1 and 2
g = acceleration of gravity, ft/sec2
d = height of bore face above the local land elevation
For areas where two-dimensional flow effects are important, velocities
(speed and direction) and water levels as a function of time can be
determined using a land inundation numerical model (Houston and Butler,
1979). Maximum elevation predictions (Houston et al., 1977; Houston
and Garcia, 1974 and 1978; Garcia and Houston, 1975) can be used as
input to the numerical model. It can be assumed that the form of the
tsunami maximum wave is approximately sinusoidal. A wave period can be
selected from historic data of tsunami activity in the area.
Forces
101. Structures may be subjected to five major forces during a
tsunami. These are bouyancy, hydrostatic, drag, surge, and impact
forces. The buoyancy force is a vertical uplifting force acting on a
structure due to the displacement of a volume of water equal to the
volume of the structure that is submerged. The hydrostatic force is a
horizontal force due to the weight and depth of water acting on the
structure. The drag force results from the flow of water past an object.
Surge forces are due to changes in either the direction or magnitude of
flow and are important when the leading edge of a surge impinges on a
structure. Impact forces are due to material carried by the flow of
water impacting a structure (U. S. Army Engineer Division, Pacific
Ocean, 1978).
102. The bouyant force is the weight of water displaced by a struc-
ture that is partially or totally submerged. The buoyant force on a
structure is given by
64
FB PgV (5)iB
where
FB = bouyant force, lb
p = density of water, lb-sec 2/ft4 (slugs/ft
3
g = acceleration of gravity, ft/sec2
V = submerged volume of the structure, ft3
Figure 15 shows the relationship between bouyant force and floor area
for a watertight building for various inundation heights. When the
bouyant force exceeds the weight of the building, it will begin to
float. An unanchored building with a floor area of 1500 sq ft with a
BOUYANT FORCE VERSUSFLOOR AREA FOR VARIOUSINUNDATION HEIGHTS h
21
Figure 15. Bouyant force(from U. S. Army Engine.!rDivision, Pacific Ocean,
1978)z
ol0
9 ,
FLOOR AREA A, SOFT
65
"dead" load of 60 psf weights 90,000 lb. This does not include the
additional weight of the building due to furnishing or other "live"
loads. If the building remains watertight (no intrusion of water),
it will begin to float at an inundation depth of only approximately
1 ft (U. S. Army Engineer Division, Pacific Ocean, 1978). Residen-
tial structures near the shoreline in Hawaii are often unanchored
and are floated off their foundations during tsunamis. In many cases,
this floating is fairly gentle, and sometimes houses can be returned to
their foundations with little repair required. Shepard et al. (1950)
reported a house at Kewela Bay, Oahu, being floated off its foundation
during the 1946 tsunami and deposited in a cane field 200 ft inland,
leaving breakfast cooking on the stove and dishes in place on shelves.
Damage caused by buoyant forces during tsunamis is often the result of
buildings being deposited on uneven ground or buildings breaking apart
when they are lifted from their foundations as a result of weak struc-
tural integrity (Peese and Matlock, 1960).
103. Hydrostatic forces are significant when stagnant of slow-
moving water piles up on one side of a wall or other barrier. The
hydrostatic force is given by
FH =1 (6)
where
FH = hydrostatic force, lb
h = depth of inundation, ft
A = projected area, ft2 (depth of inundation h times the widthof the structural member).
Since the hydrostatic pressure acting on a wall increases linearly with
depth, the force vectors have a triangular distribution. The resultant
force is located in Figure 16 at the centroid of the triangular area (a
distance of h/3 from the base). Figure 16 shows the hydrostatic force
on various widths of vertical wall for different inundation depths
(U. S. Army Engineer Division, Pacific Ocean, 1978). An imbalance in
water level of approximately 2 ft or greater can cause serious damage
to a structure. The net hydrostatic force on a solid structural member
66
I
HYDROSTATIC FORCE VERSUSINUNDATION DEPTH ON AVERTICAL WALL
70O
Sk
Figure 16. Hydrostatic 0 C
force (from U. S. Army P
Engineer Division, Pa-cific Ocean, 1978) >
20 //
0 10 15 20 25INUNDATION DEPTH h, FT
is zero if the member is surrounded by a constant depth of water.
104. Flow of water past an object produces drag forces. The drag
force is given by (U. S. Army Engineer Division, Pacific Ocean, 1978)
F P C Au 2 (7)D 2 PCDu
where
FD = drag force, lb
CD = coefficient of drag, dimensionless
Drag coefficients for flow R.s high Reynolds numbers are generally not
67
/
available, but Camfield (in preparation) used known drag coefficients to
establish maximum coefficients for design pruposes. Coefficients
generally vary from approximately 0.5 to 2.0. The drag coefficient for
a vertical wall is equal to 2.0. Figure 17 shows the force due to drag
on a 12-in.-diam pole.
105. Surge forces are important when the leading edge of a surge
impinges on a structure. The surge force is given by
2FS = P CS Au (8)
DRAG FORCE VERSUS VELOCITYFOR A 12-IN.-DIAM WOODENPOLE AT VARIOUS HEIGHTS h
WP = 12 IN. /I,
o -- . Figure 17. Drag force
(from U. S. Army Engi-0
neer Division, PacificgOcean, 1978)
_ __ /_ _
lo
VELOCITY U, FTISEC
68
whereFS = surge forces, lb
CS = surge coefficient, dimensionless
Cross (1967) relates CS to the inclination of the water surface by
the equation
Cs = (tan e) 1 . 2 + 1 (9)
where 6 is the inclination of the water surface of the surge. There-
fore, tan 6 is equal to the rate of change of the height of the
surge with the distance from the surge front. CS equals 1 for a
fairly flat surge face.
106. Impact forces are important when objects are floated by the
tsunami and impact structures. These objects may include trees,
boulders, automobiles, boats, and even buildings. Magoon (1965) indi-
cated that substantial damage occurred in Crescent City, California,
during the 1964 tsunami as a result of the collision of logs and lumber
with structures. During the 1964 tsunami, boats in the harbor at
Kodiak City, Alaska, were rammed into buildings along the waterfront.
At Whittier, Alaska, small tanks at a petroleum tank farm that were
picked up by the 1964 tsunami impacted buildings and larger tanks. The
larger tanks would have been able to withstand the direct effects of
the tsunami flow but were set into motion by the impact of the smaller
tanks and ruptured. A resulting fire destroyed the tank farm (Camfield,
in preparation).
107. The impact force caused by an object moving with the velocity
of the tsunami flow is expressed as
u2 - u1F =m At (10)
where
FI = impact force, lb
m = mass of the impact object, lb-sec /ft (slugs)
69
uI = speed of water flow (or speed of the object if it ismoving at a lesser speed), ft/sec
u2 = speed of object after impact with a structure (equal to zeroif structure remains fixed after impact), ft/sec
At = time interval of impact, sec
108. The impact time may be very short if both the object and the
structure are rigid. If either the object or structure deforms upon
impact, the time interval may be significantly greater than for the
collision of rigid objects. In the handbook published by the U. S.
4Army Engineer Division, Pacific Ocean (1978), the time interval of
impact is estimated to usually vary between 0.01 to 1.0 sec. Figure 18
shows the relationship between velocity and impact force for a 1000-lb
object and a 1.0-sec impact time.
70
IMPACT FORCEVERSUS VELOCITY
1400
I10-LB OBJECT
low
0/
VELOCITY U, FT/SEC
Figure 18. Impact force (from U. S. ArmyEngineer Division, Pacific Ocean, 1978)
7i
Il
PART VII: SEICHES
Introduction
109. Seiching of enclosed bodies of water often occurs following
an earthquake. Reid (1914) reported that the power of an earthquake to
cause seiching in lakes, ponds, and canals was first noticed at the
time of the Lisbon earthquake of 1755. This earthquake excited seiching
motions in small bodies of water throughout Europe as far away from
Portugal as Finland. Reid attributed the seiching motion to a
synchronism of period between the long-period surface waves produced by
the earthquake and natural periods of oscillation of the bodies of water.
The ability of earthquakes to produce seiching in bodies of water at
tremendous distances from the epicenter also was noted during the Assam
(eastern India) earthquake of 1950 that produced seiching in Norway and
England (Kvale, 1955).
110. The 1964 Alaskan earthquake caused extensive seiche action in
lakes, ponds, canals, rivers, waterways, and swimming pools all along
the Louisiana coast and along the Texas coast as far west as Freeport.
Although damage was gradually minor, it was very widespread along this
part of the Gulf Coast of the United States. There were many reports of
boats breaking their mooring lines and sinking or damaging piers, docks,
and marine service facilities. A small U. S. Corps of Engineers boat
was destroyed near Morgan City, Louisiana, when it was crushed between
another boat and a tree on the bank as a result of a 4-ft seiche. Waves
1 to 5 ft in height were reported at many locations (Spaeth and Berkman,
1967). Donn (196h) and McGarr (1965) attributed these seiches reported
on the Gulf Coast and seiches reported in two reservoirs in Arkansas to
excitations induced by arrival of Love or Rayleigh waves. The ampli-
tudes of these surface waves were very large on the Gulf Coast with
almost all of the seismographs in this region used to measure surface
waves driven off scale. The unusually large amplitudes are believed to
be related to the great thickness of sediment in the Gulf Coast region.
The amplitude of the seiching motion induced in a body of water is
72
-1 1. - _ _ - - -
*dependent upon the amplitude of the long-period surfbce waves generated
by the earthquake and the similarity between the period of the surface
waves and the natural periods of oscillation of the body of water.
111. More dramatic seiching motion may be produced by a permanent
vertical ground displacement occurring in an enclosed body of water.
For example, on 17 August 1959 an earthquake with a magnitude of 7.1
occurred at Hebgen Lake in southern Montana. It has been estimated that
the lake bottom dropped a distance of 10 ft at Hebgen Dam and up to
4j7 19 to 21 ft approximately 4 miles upstream (Wiegel and Camotim, 1962).
This displacement of the bottom of the lake produced a seiching motion
in the lake. At the dam, iwater alternately flowed over the dam and thenflowed away leaving exposed the lake bottom near the dam. Water proba-
*. bly flowed over the dam four times with a maximum height of 4 ft or
more. Each flow of water over the dam lasted from 10 to 20 min. The
rush of water down the back of the dam produced some erosion, particu-
larly at the base of the dam. A small powerhouse at the base of the
dam was filled with debris carried by the water, and the spillway (which
also may have been directly damaged by the earthquake) was damaged as a
result of the erosion of earth beneath some concrete slabs (Steinbrugge
and Clould, 1962).
Modeling of Seiches
112. One of the few attempts to model seiching activity in an
enclosed body of water induced by earthquake activity was a hydraulic
model investigation by Wiegel and Camotim (1962) of seiching in Hebgen
Lake during the 17 August 1959 earthquake. This model was constructed
of wood and was distorted, with the horizontal scale about 1:8000
and the vertical scale about 1:3500. The sidewalls of the model were
vertical, and the bottom was either sloping uniformly or horizontal.
The action of the earthquake was simulated by dropping the end of the
model corresponding to the dam. The small scale of the model resulted
in severe damping; thus, the duration and amplitudes of the seiching
could not be accurately modeled.
73
113. Numerical models can be used to study seiching in enclosed
bodies of water. Since the oscillations have a long period, long waves
govern the motion. Seiching induced by horizontal shaking of an enclosed
body of water can be studied using a numerical model developed by Lee and
Hwang (1978). The enclosed body of water must have a constant depth.
Seiching produced by a permanent vertical ground displacement can be
studied using any of the tsunami numerical models discussed in Part III.
Since reservoirs usually have very complicated shapes, a finite element
model, such as that developed by Kawahara et al. (1978), would be ad-
vantageous since the finite element method uses very flexible grids that
allow complicated shapes to be well represented. Finite element models,
such as those developed by Desai and Abel (1972) and Patil (1970), that
solve free oscillation problems also can be used for seiching problems.
These models require little computational time. The model of Desai and
Abel has been used to study seiching induced by atmospheric phenomena
in Lake Erie by Raney et al. (1974). An arbitrary vertical displacement
can be separated into free modes of oscillation and elevations at later
times throughout the reservoir region determined using an approach
described by Wilson (1975).
74
I/
PART VIII: LANDSLIDE-INDUCED WATER WAVES
Introduction
114. Landslide-induced water waves can occur in coastal regions,
enclosed bodies of water such as lakes or reservoirs, and rivers. These
waves are a potential problem where steep inclines border water. Land-
slides can be generated by earthquakes, water saturation of soil, and
other effects. Slides down marine slopes, known as subaqueous slides,
also can generate destructive waves.
115. Landslide-induced water waves have produced great destruction
in the past. In 1792, a landslide of approximately 700 million cubic
yards of rock and soil fell into Shimabara Bay, Japan. Waves as large
as 33 ft produced destruction along 50 miles of the shores of the bay.
Trees with diameters as great as 9 ft were snapped by the tremendous
forces. More than 15,000 people were killed, most of them by the waves.
In 1756, a landslide in Langfjord, Norway, produced waves with heights
as great as 130 ft. Effects of the waves were noticed at distances of
25 miles, and 32 people were killed. A series of landslides in Loen
Lake and TafJord, Norway, from 1905 through 1934 produced waves that
killed over 178 people (Miller, 1960).
116. One of the great disasters of modern times occurred in 1963
when a rock slide fell into a reservoir in the Vaiont Valley, Italy.
Approximately 310 million cubic yards of rock slid into the reservoir
and filled the first 1.5 miles of the reservoir. The slide displaced a
tremendous quantity of water that flowed over the dam. Although the dam
itself was essentially undamaged, the water that flowed over the dam
formed a flood wave that destroyed the city of Langarome in the Piave
Valley and killed 3000 people. A large water wave generated by the
landslide also traveled upstream and damaged a number of buildings in
two villages (Wiegel, 1976).
117. Several large landslides have generated significant waves in
the United States. In 1905, a hanging glacier fell into Disenchantment
Bay, Alaska, producing waves with heights as great as 115 ft. Several
75
slides between 1944 and 1953 fell into Franklin D. Roosevelt Lake in
the Columbia River valley and produced waves with heights as great as
65 ft. The highest wave that has been documentedwas generated in 1958
by a landslide that was triggered by an earthquake and slid into Lituya
Bay, Alaska. The landslide generated a wave that reached an elevation
of 1740 ft on the opposite side of the bay and stripped the hillside of
trees that were 50 ft high. Similar slides generated waves in Lituya
Bay in 1853, 1874, and 1936 (Miller, 1960).
118. Subaqueous landslides triggered by the 1964 Alaskan tsunamicaused widespread damage in Alaska. The city of Whittier, Alaska, was
completely destroyed by waves as great as 104 ft in elevation generated
by a submarine slide. Subaqueous slides produced runup elevations as
great as 220 ft at Port Valdez, Alaska (Wilson and Torum, 1964).
119. In addition to generating large waves, landslides can cause
serious problems by damming rivers and thus creating natural reservoirs.
Once these reservoirs fill from the riverine flow, the dam is overtopped
and a rapid washout of the natural dam can cause disasterous flooding
downstream. Landslides into rivers occur quite often. For example,
in 1970, a slide of about 2 million cubic yards of material moved down-
ward about 3200 ft and then slid across the South Fork of the Smith
River in California. A few weeks later, a slide of several hundred
thousand cubic yards moved 1700 ft in a few seconds down to the Eel
River in California and then continued 650 ft across the river channel
(Wiegel, 1976). In 1927, a landslide at Gros Ventre, Wyoming, blocked
a river and created a natural dam. Once the reservoir filled, the dam
was overtopped and washed out rapidly, resulting in a disasterous flood
that killed several people in Kelly, Wyoming. During the earthquake at
Hebgen Lake, Montana, in 1959, a rockslide in the Madison Canyon down-
stream from the Hebgen Lake Dam blocked water that overflowed the dam
during seiching of Hebgen Lake. Remembering the disaster created by
the Gros Ventre landslide of 1927, the U. S. Army Corps of Engineers
reduced the height of the rockslide at Madison Canyon and thus the
likelihood of a serious downstream flooding that might occur if a reser-
voir formed behind the rockslide (Steinbrugge and Cloud, 1962).
76
Modeling of Landslides
Hydraulic models
120. In addition to general hydraulic model studies of the dropping
of rectangular boxes (representing rockslides) into bodies of water by
Wiegel et al. (1970), hydraulic model tests of landslides have been per-
formed using scale models of actual reservoirs. For example, a study of
possible high-speed rockslides into the reservoir created by the Mica
Dam on the Columbia River was performed using a hydraulic model (Western
Canada Hydraulic Laboratories Ltd., 1970). In addition to investigating
the waves generated by landslides, this study investigated the erosion
resistance of the dam during overtopping by these waves. A study of
landslides into Lake Koocanusa, Montana, was performed by Davidson and
Whalin (1974) using a 1:120 undistorted scale model of Libby Dam and
Lake Koocanusa. The magnitude of wave heights, runup along the sides
of the lake, and overtopping of the dam were determined for four
potential landslides. Bags of iron ore and lead were mixed to reproduce
the correct rock density, and the bags were placed on an inclined
plane slope to obtain the correct elevation-volume-shape relationship.
A major advantage of using hydraulic models for modeling landslides
is that the large amplitude and short-period waves generated by the
landslide are accurately modeled in an undistorted and large-scale model.
Numerical models
121. The relatively short wavelengths and large amplitudes of
landslide-induced water waves make it difficult to model them numerically.
Noda (1970) developed a one-dimensional numerical solution of an inte-
gral equation that described landslide-induced water waves generated by
simple falling bodies. Koutitas (1977) developed a one-dimensional
finite element model and applied it to the case of a long narrow channel
where a lateral landslide caused a sudden change of its cross section.
Koutitas and Xanthopoulos (1978) developed a two-dimensional finite
element numerical model that solved nonlinear long-wave equations.
Raney and Butler (1975 and 1977) developed a two-dimensional finite dif-
ference model that solved nonlinear long-wave equations. They made
77
Lo
71
comparisons between numerical model calculations and the hydraulic model
tests conducted by Davidson and Whalin (1974). Reasonable agreement was
found between the leading (largest) wave calculated by the numerical
model and measurements of Davidson and Whalin. Raney and Butler (1977)
concluded that for small landslide velocities, the viscous drag and
pressure drag contributions to wave heights and velocities are small,
and that the physical displacement of the water by the landslide is the
predominant factor. The water waves produced by the slide for this con-
dition will generally propagate faster than the motion of the slide;
thus, the initial phase of the landslide as it enters the water must be
accurately defined if good numerical results are to be obtained. How-
ever, for large landslide velocities, significant contributions to wave
heights and propagation velocities are produced by the viscous drag and
pressure drag. Viscous and pressure drag contributions to wave heights
and velocities are focused in the direction of the landslide to a
greater degree than the contributions from the physical displacement of
water. If the landslide is moving faster than the normal propagation
velocity of the water waves it produces, the entire path and time history
of the landslide becomes important in obtaining an accurate prediction
of the first wave crest.
78
*.m m - m.- -- . .... . . . ....F .
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88
APPENDIX A: NOTATION
I2A Tsunami amplitude, ft; projected area,
ft2
C Dimensionless number
C Coefficient of drag, dimensionlessD
CS Surge coefficient, dimensionless
d Height of bore face above local land elevation
D Number of years
F Frequency per year of tsunami occurrence
FB Buoyant force, lb
FD Drage force, lb
FH Hydrostatic force, lb
F Impact force, lbI
FS Surge force, lb
g Acceleration of gravity, ft/sec2
h Depth of inundation, ft
H Tsunami wave height in the direction of the major axis of asource of length a
Hb Tsunami wave height in the direction of the minor axis of asource of length b
H Average runup over a coast, mave
i Tsunami intensity
i Tsunami intensity for particular tsunami
i2 Tsunami intensity for particular tsunami
m Mass of impact object, lb-sec 2/ft (slugs)
P Probability
a Ground slope
Al
t Time, sec
T Tsunami period, sec
1t Time interval uf impact, sec
u Horizontal speed, ft/sec
uI Speed of water flow, ft/sec
u2 Speed of object after impact with a structure, ft/sec
V Submerged volume of the structure, ft3
e Inclination of the water surface of a surge
p Density of water, lb-sec 2/ft (slugs/ft3
A2
MnOM,,,M
II i
In accordance with letter from DAEN-RDC, DAEN-ASI dated22 July 1977, Subject: Facsimile Catalog Cards forLaboratory Technical Publications, a facsimile catalogcard in Library of Congress MARC format is reproducedbelow.
Houston, James RState-of-the-art for assessing earthquake hazards in the
United States; Report 15: Tsunamis, seiches, and landslide-induced water waves / by James R. Houston. Vicksburg, Miss.U. S. Waterways Experiment Station ; Springfield, Va. : avail-able from National Technical Information Service, 1979.
88, 2 p. : ill. ; 27 cm. (Miscellaneous paper - U. S. ArmyEngineer Waterways Experiment Station ; S-73-1, Report 15)
Prepared for Office, Chief of Engineers, U. S. Army, Wash-ington, D. C.References: p. 79-88.
1. Earthquake damage. 2. Earthquake engineering. 3. Earth-quake hazards. 4. Landslides. 5. Seiches. 6. State-of-the-art studies. 7. Tsunamis. 8. Water waves. I. United States.Army. Corps of Engineers. II. Series: United States. Water-ways Experiment Station, Vicksburg, Miss. Miscellaneous paperS-73-1, Report 15.TA7.W34m no.S-73-1 Report 15
